Math Wiki - User contributions [en]

Welcome to the UCR Math Wiki

2015-03-10T00:26:22Z

WikiSysop: /* Welcome to the UCR Math Wiki! */

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 23px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math Wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
'''[[Courses]]'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:RegularRhombs.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''[[Challenge Problems]]'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
[[File:Category150px.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''[[Concepts]]'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Saddlept.jpg]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''[[Historical Notes]]'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

Welcome to the UCR Math Wiki

2015-03-02T21:34:01Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 23px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math Wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
'''[[Courses]]'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:RegularRhombs.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
[[File:Category150px.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Saddlept.jpg]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

Welcome to the UCR Math Wiki

2015-03-02T21:00:47Z

WikiSysop: /* Welcome to the UCR Math Wiki! */

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 23px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math Wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:RegularRhombs.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
[[File:Category150px.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Saddlept.jpg]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

Welcome to the UCR Math Wiki

2015-03-02T19:03:13Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 23px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:RegularRhombs.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
[[File:Category150px.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Saddlept.jpg]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

Welcome to the UCR Math Wiki

2015-03-02T19:03:01Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 20px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:RegularRhombs.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
[[File:Category150px.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Saddlept.jpg]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

Welcome to the UCR Math Wiki

2015-03-02T18:53:15Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 25px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:RegularRhombs.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
[[File:Category150px.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Saddlept.jpg]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

File:Saddlept.jpg

2015-03-02T18:52:57Z

WikiSysop:

Welcome to the UCR Math Wiki

2015-03-02T18:51:16Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 25px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:RegularRhombs.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
[[File:Category150px.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Parabolic particle.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

File:Category150px.png

2015-03-02T18:50:51Z

WikiSysop:

Welcome to the UCR Math Wiki

2015-03-02T18:50:24Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 25px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:RegularRhombs.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
[[File:Diagram.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Parabolic particle.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

File:RegularRhombs.png

2015-03-02T18:50:06Z

WikiSysop:

Welcome to the UCR Math Wiki

2015-03-02T18:47:58Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 25px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Penrose-tiling-Rhombi.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 150px; background-color: white;text-align:center;"|
[[File:Diagram.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
[[File:Parabolic particle.png]]
| style="width: 25%; height:150px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

Welcome to the UCR Math Wiki

2015-03-02T18:47:21Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 25px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 300px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
[[File:Penrose-tiling-Rhombi.png]]
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
[[File:Gauss150px.jpg]]
|-
| style="width: 25%; height: 300px; background-color: white;text-align:center;"|
[[File:Diagram.png]]
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
[[File:Parabolic particle.png]]
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

File:Gauss150px.jpg

2015-03-02T18:47:02Z

WikiSysop:

Welcome to the UCR Math Wiki

2015-03-02T01:30:03Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 25px;" width="100%"
| colspan="4" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 300px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
[[File:Penrose-tiling-Rhombi.png]]
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
[[File:Gauss.png]]
|-
| style="width: 25%; height: 300px; background-color: white;text-align:center;"|
[[File:Diagram.png]]
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
[[File:Parabolic particle.png]]
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}
{| style="color: black; background-color: #f1ab00; height: 48px;" width="100%"
| colspan="4" |
|}
{| style="color: white; background-color: #2d6cc0; height: 50px;text-align:center;" width="100%"
| colspan="4" | Any questions, corrections or comments should be sent to wiki@math.ucr.edu
|}

Welcome to the UCR Math Wiki

2015-03-02T01:23:20Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="2" |
|}
{| style="color: black; background-color: #f1ab00; height: 50px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 300px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
[[File:Penrose-tiling-Rhombi.png]]
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
[[File:Gauss.png]]
|-
| style="width: 25%; height: 300px; background-color: white;text-align:center;"|
[[File:Diagram.png]]
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
[[File:Parabolic particle.png]]
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}

File:Gauss.png

2015-03-02T01:22:48Z

WikiSysop:

File:Diagram.png

2015-03-02T01:20:53Z

WikiSysop: Its a diagram. I don't know, your the smart one.

Its a diagram. I don't know, your the smart one.

Welcome to the UCR Math Wiki

2015-03-02T01:15:36Z

WikiSysop: /* Welcome to the UCR Math Wiki! */

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #2d6cc0; height: 50px;" width="100%"
| colspan="2" |
|}
{| style="color: black; background-color: #f1ab00; height: 300px; text-align:center;" width="100%"
| colspan="4"|'''The UCR Math wiki is operated and maintained by mathematics graduate students'''
|-
| style="width: 25%; height: 300px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Historical Notes'''
|-
| style="width: 25%; height: 300px; background-color: white;text-align:center;"|
'''Courses'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Concepts'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Challenge Problems'''
| style="width: 25%; height:300px; background-color: white;text-align:center;"|
'''Historical Notes'''
|}

Welcome to the UCR Math Wiki

2015-03-02T00:16:37Z

WikiSysop:

== Welcome to the UCR Math Wiki! ==

{| style="color: black; background-color: #f1ab00;" width="100%"
| colspan="2" |

Welcome to the UCR Math Wiki

2015-03-01T23:42:26Z

WikiSysop: Blanked the page

Welcome to the UCR Math Wiki

2015-03-01T23:40:28Z

WikiSysop: WikiSysop moved page Main Page to University of California Riverside Math Wiki

#REDIRECT [[University of California Riverside Math Wiki]]

File:Parabolic particle.png

2015-02-27T21:56:45Z

WikiSysop:

File:Penrose-tiling-Rhombi.png

2015-02-27T21:49:00Z

WikiSysop:

Prototype questions

2015-02-23T21:57:54Z

WikiSysop:

2. Find the domain of the following function. Your answer should use interval notation.
f(x) = <math> \displaystyle{\frac{1}{\sqrt{x^2-x-2}}} </math>

{| class="mw-collapsible mw-collapsed"
! Foundations
|-
|'''The foundations:'''
|-
| What is the domain of g(x) = <math>\frac{1}{x}</math>?
|-
|The function is undefined if the denominator is zero, so x <math>\neq </math> 0.
|-
|Rewriting" <math>x \neq 0</math>" in interval notation( -<math>\infty</math>, 0) <math>\cup</math>(0, <math>\infty</math>)
|-
|What is the domain of h(x) = <math> \sqrt{x} </math>?
|-
|The function is undefined if we have a negative number inside the square root, so x <math>\ge</math> 0
|}

Solution:

{| class = "mw-collapsible mw-collapsed"
! Step 1:
|-
|Factor <math>x^2 - x - 2</math>
|-
|<math> x^2 - x - 2 = (x + 1) (x - 2)</math>
|-
| So we can rewrite f(x) as <math>f(x) = \displaystyle{\frac{1}{\sqrt{(x+1)(x-2)}}}</math>
|}

{|class = "mw-collapsible mw-collapsed"
! Step 2:
|-
|When does the denominator of f(x) = 0?
|-
|<math>\sqrt{(x + 1)(x - 2)} = 0</math>
|-
|(x + 1)(x - 2) = 0
|-
|(x + 1) = 0 or (x - 2) = 0
|-
|x = -1 or x = 2
|-
|So, since the function is undefiend when the denominator is zero, x <math>\neq</math> -1 and x <math>\neq</math> 2
|}

{|class = "mw-collapsible mw-collapsed"
! Step 3:
|-
|What is the domain of <math>h(x) = \sqrt{(x + 1)(x - 2)}</math>
|-
|critical points: x = -1, x = 2
|-
|Test points:
|-
|x = -2: (-2 + 1)(-2 - 2): (-1)(-4) = 4 > 0
|-
|x = 0: (0 + 1)(0 - 2) = -2 < 0
|-
|x = 3: (3 + 1)(3 - 2): 4*1 = 4 > 0
|-
|So the domain of h(x) is <math>(-\infty, -1] \cup [2, \infty)</math>
|}

{|class = "mw-collapsible mw-collapsed"
! Step 4:
|-
|Take the intersection (i.e. common points) of Steps 2 and 3. <math>( - \infty, -1) \cup (2, \infty)</math>
|}

2. Find the domain of the following function. Your answer should use interval notation.
f(x) = <math> \displaystyle{\frac{1}{\sqrt{x^2-x-2}}} </math>

{| class="mw-collapsible mw-collapsed wikitable"
! Foundations
|-
|'''The foundations:'''
|-
| What is the domain of g(x) = <math>\frac{1}{x}</math>?
|-
|The function is undefined if the denominator is zero, so x <math>\neq </math> 0.
|-
|Rewriting"x <math>\neq</math> 0" in interval notation( -<math>\infty</math>, 0) <math>\cup</math>(0, <math>\infty</math>)
|-
|What is the domain of h(x) = <math> \sqrt{x} </math>?
|-
|The function is undefined if we have a negative number inside the square root, so x <math>\ge</math> 0
|}

Solution:

{| class = "mw-collapsible mw-collapsed wikitable"
! Step 1:
|-
|Factor <math>x^2 - x - 2</math>
|-
|<math> x^2 - x - 2 = (x + 1) (x - 2)</math>
|-
| So we can rewrite f(x) as <math>f(x) = \displaystyle{\frac{1}{\sqrt{(x+1)(x-2)}}}</math>
|}

{|class = "mw-collapsible mw-collapsed wikitable"
! Step 2:
|-
|When does the denominator of f(x) = 0?
|-
|<math>\sqrt{(x + 1)(x - 2)} = 0</math>
|-
|(x + 1)(x - 2) = 0
|-
|(x + 1) = 0 or (x - 2) = 0
|-
|x = -1 or x = 2
|-
|So, since the function is undefinend when the denominator is zero, x <math>\neq</math> -1 and x <math>\neq</math> 2
|}

{|class = "mw-collapsible mw-collapsed wikitable"
! Step 3:
|-
|What is the domain of <math>h(x) = \sqrt{(x + 1)(x - 2)}</math>
|-
|critical points: x = -1, x = 2
|-
|Test points:
|-
|x = -2: (-2 + 1)(-2 - 2): (-1)(-4) = 4 > 0
|-
|x = 0: (0 + 1)(0 - 2) = -2 < 0
|-
|x = 3: (3 + 1)(3 - 2): 4*1 = 4 > 0
|-
|So the domain of h(x) is <math>(-\infty, -1] \cup [2, \infty)</math>
|}

{|class = "mw-collapsible mw-collapsed wikitable"
! Step 4:
|-
|Take the intersection (i.e. common points) of Steps 2 and 3. <math>( - \infty, -1) \cup (2, \infty)</math>
|}

2. Find the domain of the following function. Your answer should use interval notation.
<math>f(x) = \displaystyle{\frac{1}{\sqrt{x^2-x-2}}}</math>

{| class="mw-collapsible mw-collapsed"
! Hint 1
|-
| Which x-values lead to division by 0 or square rooting a negative number
|}

{| class="mw-collapsible mw-collapsed"
! Hint 2
|-
| Use a sign chart to determine for which x-values <math>x^2-x-2 > 0</math>
|}

Solution:
{| class="mw-collapsible mw-collapsed"
! Solution
|-
| Since the domain is the collection of x-values for which we don't divide by zero or square root a negative number we want to solve the inequality <math>x^2 - x - 2 > 0</math>
|-
|<math>(x-2)(x+1)>0</math>
|-
|Now we use a sign chart with test numbers -2, 0, and 3
|-
|<math>x = -2: (-2 - 2)(-2 + 1) = (-4)(-1) = 4 > 0</math>
|-
|<math>x = 0: (0 - 2)(0 + 1) = (-2)(1) = -2 < 0</math>
|-
|<math>x = 3: (3 - 2)(3 + 1)= (1)(4) = 4 > 0</math>
|-
|So the solution is <math>(-\infty, -1) \cup (2, \infty)</math>
|}

2. Find the domain of the following function. Your answer should use interval notation.
<math>f(x) = \displaystyle{\frac{1}{\sqrt{x^2-x-2}}}</math>

{| class="mw-collapsible mw-collapsed wikitable"
! Hint 1
|-
| Which x-values lead to division by 0 or square rooting a negative number
|}

{| class="mw-collapsible mw-collapsed wikitable"
! Hint 2
|-
| Use a sign chart to determine for which x-values <math>x^2-x-2 > 0</math>
|}

Solution:
{| class="mw-collapsible mw-collapsed wikitable"
! Solution
|-
| Since the domain is the collection of x-values for which we don't divide by zero or square root a negative number we want to solve the inequality <math>x^2 - x - 2 > 0</math>
|-
|<math>(x-2)(x+1)>0</math>
|-
|Now we use a sign chart with test numbers -2, 0, and 3
|-
|<math>x = -2: (-2 - 2)(-2 + 1) = (-4)(-1) = 4 > 0</math>
|-
|<math>x = 0: (0 - 2)(0 + 1) = (-2)(1) = -2 < 0</math>
|-
|<math>x = 3: (3 - 2)(3 + 1)= (1)(4) = 4 > 0</math>
|-
|So the solution is <math>(-\infty, -1) \cup (2, \infty)</math>
|}

Prototype questions

2015-02-23T21:57:23Z

WikiSysop:

Naming Conventions

2015-02-22T02:43:35Z

WikiSysop: Created page with "This page should have the conventions for how we name uploaded files and pages. Pages will be of ideally a few types, right now the only two that occur to me are courses and..."

This page should have the conventions for how we name uploaded files and pages.

Pages will be of ideally a few types, right now the only two that occur to me are courses and concepts.

course pages will follow the page naming convention

MATHCOURSE with the course number padded with leading 0s to make it 3 digits long. So 9A would be MATH009A

TestPage

2015-02-11T23:57:48Z

WikiSysop: Protected "TestPage" ([edit=sysop] (indefinite) [move=sysop] (indefinite))

This is a test page

I'm going to write some math

<math>E(|A\cap B|) = n * P(i \in A\cap B) = n* \left(\frac{\binom{N-1}{n-1}}{\binom{N}{n}}\right)^2 = \frac{n^3}{N^2}</math>

I hope that works

TestPage

2015-02-11T23:56:41Z

WikiSysop: Created page with "This is a test page I'm going to write some math <math>E(|A\cap B|) = n * P(i \in A\cap B) = n* \left(\frac{\binom{N-1}{n-1}}{\binom{N}{n}}\right)^2 = \frac{n^3}{N^2}</math> I…"

This is a test page

I'm going to write some math

<math>E(|A\cap B|) = n * P(i \in A\cap B) = n* \left(\frac{\binom{N-1}{n-1}}{\binom{N}{n}}\right)^2 = \frac{n^3}{N^2}</math>

I hope that works