009A Sample Final 1 - Revision history

MathAdmin at 16:05, 10 April 2017

2017-04-10T16:05:51Z

2016-04-18T20:26:12Z

2016-04-18T19:01:34Z

Problem 2

2016-04-18T18:57:03Z

Problem 10

2016-04-18T18:56:42Z

Problem 9

2016-04-18T18:56:18Z

Problem 8

2016-04-18T18:56:00Z

Problem 7

2016-04-18T18:55:37Z

Problem 2

2016-04-18T18:55:24Z

Problem 4

2016-04-18T18:54:59Z

Problem 6

← Older revision		Revision as of 20:26, 18 April 2016
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−	'''This is a sample, and is meant to represent the material usually covered in Math 9A for the final. An actual test may or may not be similar. Click on the''' '''<span class="biglink" style="color:darkblue;"> boxed problem numbers </span> to go to a solution.'''	+	'''This is a sample, and is meant to represent the material usually covered in Math 9A for the final. An actual test may or may not be similar.'''
		+
		+	'''Click on the''' '''<span class="biglink" style="color:darkblue;"> boxed problem numbers </span> to go to a solution.'''
	<div class="noautonum">__TOC__</div>		<div class="noautonum">__TOC__</div>

@@ Line 21: / Line 21: @@
     \right.
 </math>
-::<span class="exam">a) Show that <math style="vertical-align: -5px">f(x)</math> is continuous at <math style="vertical-align: 0px">x=3</math>.
+::<span class="exam">a) Show that <math style="vertical-align: -5px">f(x)</math> is continuous at <math style="vertical-align: 0px">x=3.</math>
-::<span class="exam">b) Using the limit definition of the derivative, and computing the limits from both sides, show that <math style="vertical-align: -5px">f(x)</math> is differentiable at <math style="vertical-align: 0px">x=3</math>.
+::<span class="exam">b) Using the limit definition of the derivative, and computing the limits from both sides, show that <math style="vertical-align: -5px">f(x)</math> is differentiable at <math style="vertical-align: 0px">x=3.</math>
 == [[009A_Sample Final 1,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==

@@ Line 92: / Line 92: @@
 <span class="exam">defined on the closed, bounded interval <math style="vertical-align: -5px">[-8,8]</math>.
-<span class="exam">a) Find all the critical points for <math style="vertical-align: -5px">f(x)</math>.
+::<span class="exam">a) Find all the critical points for <math style="vertical-align: -5px">f(x)</math>.
-<span class="exam">b) Determine the absolute maximum and absolute minimum values for <math style="vertical-align: -5px">f(x)</math> on the interval <math style="vertical-align: -5px">[-8,8]</math>.
+::<span class="exam">b) Determine the absolute maximum and absolute minimum values for <math style="vertical-align: -5px">f(x)</math> on the interval <math style="vertical-align: -5px">[-8,8]</math>.
 '''Contributions to this page were made by [[Contributors|Kayla Murray]]'''

@@ Line 73: / Line 73: @@
 == [[009A_Sample Final 1,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==
-<span class="exam">Given the function <math style="vertical-align: -5px">f(x)=x^3-6x^2+5</math>,
+::<span class="exam">Given the function <math style="vertical-align: -5px">f(x)=x^3-6x^2+5</math>,
-<span class="exam">a) Find the intervals in which the function increases or decreases.
+::<span class="exam">a) Find the intervals in which the function increases or decreases.
-<span class="exam">b) Find the local maximum and local minimum values.
+::<span class="exam">b) Find the local maximum and local minimum values.
-<span class="exam">c) Find the intervals in which the function concaves upward or concaves downward.
+::<span class="exam">c) Find the intervals in which the function concaves upward or concaves downward.
-<span class="exam">d) Find the inflection point(s).
+::<span class="exam">d) Find the inflection point(s).
-<span class="exam">e) Use the above information (a) to (d) to sketch the graph of <math style="vertical-align: -5px">y=f(x)</math>.
+::<span class="exam">e) Use the above information (a) to (d) to sketch the graph of <math style="vertical-align: -5px">y=f(x)</math>.
 == [[009A_Sample Final 1,_Problem_10|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 10&nbsp;</span>]] ==

@@ Line 67: / Line 67: @@
 ::::::<math>y=x^3.</math>
-<span class="exam">a) Find the differential <math style="vertical-align: -4px">dy</math> of <math style="vertical-align: -4px">y=x^3</math> at <math style="vertical-align: 0px">x=2</math>.
+::<span class="exam">a) Find the differential <math style="vertical-align: -4px">dy</math> of <math style="vertical-align: -4px">y=x^3</math> at <math style="vertical-align: 0px">x=2</math>.
-<span class="exam">b) Use differentials to find an approximate value for <math style="vertical-align: -1px">1.9^3</math>.
+::<span class="exam">b) Use differentials to find an approximate value for <math style="vertical-align: -1px">1.9^3</math>.
 == [[009A_Sample Final 1,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==

@@ Line 57: / Line 57: @@
 ::::::<math>x^3+y^3=6xy.</math>
-<span class="exam">a) Using implicit differentiation, compute &thinsp;<math style="vertical-align: -12px">\frac{dy}{dx}</math>.
+::<span class="exam">a) Using implicit differentiation, compute &thinsp;<math style="vertical-align: -12px">\frac{dy}{dx}</math>.
-<span class="exam">b) Find an equation of the tangent line to the curve <math style="vertical-align: -4px">x^3+y^3=6xy</math> at the point <math style="vertical-align: -5px">(3,3)</math>.
+::<span class="exam">b) Find an equation of the tangent line to the curve <math style="vertical-align: -4px">x^3+y^3=6xy</math> at the point <math style="vertical-align: -5px">(3,3)</math>.
 == [[009A_Sample Final 1,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==

@@ Line 14: / Line 14: @@
 <span class="exam"> Consider the following piecewise defined function:
-::::<math>f(x) = \left\{
+::::::<math>f(x) = \left\{
       \begin{array}{lr}
         x+5 &  \text{if }x < 3\\

@@ Line 35: / Line 35: @@
 <span class="exam"> If
-::<math>y=x^2+\cos (\pi(x^2+1)),</math>
+::::::<math>y=x^2+\cos (\pi(x^2+1)),</math>
 <span class="exam">compute &thinsp;<math style="vertical-align: -12px">\frac{dy}{dx}</math>&thinsp; and find the equation for the tangent line at <math style="vertical-align: -3px">x_0=1</math>. You may leave your answers in point-slope form.

@@ Line 47: / Line 47: @@
 ::::::<math>f(x)=3x-2\sin x+7</math>
-<span class="exam">a) Use the Intermediate Value Theorem to show that <math style="vertical-align: -5px">f(x)</math> has at least one zero.
+::<span class="exam">a) Use the Intermediate Value Theorem to show that <math style="vertical-align: -5px">f(x)</math> has at least one zero.
-<span class="exam">b) Use the Mean Value Theorem to show that <math style="vertical-align: -5px">f(x)</math> has at most one zero.
+::<span class="exam">b) Use the Mean Value Theorem to show that <math style="vertical-align: -5px">f(x)</math> has at most one zero.
 == [[009A_Sample Final 1,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==