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- 14:37, 1 February 2016 diff hist +1,519 N 009B Sample Midterm 1, Problem 4 Created page with "<span class="exam">Evaluate the integral: ::<math>\int \sin^3x \cos^2x~dx</math> {| class="mw-collapsible mw-collapsed" style = "text-align:left;" !Foundations: |-..."
- 14:37, 1 February 2016 diff hist +2,600 N 009B Sample Midterm 1, Problem 3 Created page with "<span class="exam">Evaluate the indefinite and definite integrals. ::<span class="exam">a) <math>\int x^2 e^x~dx</math> ::<span class="exam">b) <math>\int_{1}^{e} x^3\ln x~d..."
- 14:36, 1 February 2016 diff hist +2,318 N 009B Sample Midterm 1, Problem 2 Created page with "<span class="exam">Find the average value of the function on the given interval. ::<math>f(x)=2x^3(1+x^2)^4,~~~[0,2]</math> {| class="mw-collapsible mw-collapsed" style = "..."
- 14:34, 1 February 2016 diff hist +2,536 N 009B Sample Midterm 1, Problem 1 Created page with "<span class="exam">Evaluate the indefinite and definite integrals. ::<span class="exam">a) <math>\int x^2\sqrt{1+x^3}~dx</math> ::<span class="exam">b) <math>\int _{\frac{\pi..."
- 14:34, 1 February 2016 diff hist +2,232 N 009B Sample Midterm 1 Created page with "'''This is a sample, and is meant to represent the material usually covered in Math 9B for the midterm. An actual test may or may not be similar. Click on the''' '''<span clas..."
- 13:14, 29 November 2015 diff hist +1,225 N Systems of Nonlinear Equations Created page with "<div class="noautonum">__TOC__</div> ==Comparison to linear systems== Systems of nonlinear equations are solved using the same methods we used to solve linear systems, elimin..." current
- 13:13, 29 November 2015 diff hist +78 Math 5 →Concepts current
- 23:07, 28 November 2015 diff hist +1,508 N Systems of Linear Equations Created page with "<div class="noautonum">__TOC__</div> ==Geometric idea/Introduction== We want to know when a collection of lines has a point that lies on all of the lines. There are three pos..." current
- 23:06, 28 November 2015 diff hist +102 Math 5
- 20:01, 26 November 2015 diff hist 0 File:5 Sample Final 20.png MathAdmin uploaded a new version of File:5 Sample Final 20.png current
- 19:56, 26 November 2015 diff hist 0 File:5 Sample Final 20.png MathAdmin uploaded a new version of File:5 Sample Final 20.png
- 17:45, 23 November 2015 diff hist 0 Implicit Differentiation →Exercise 2: Find equation of tangent line current
- 17:42, 23 November 2015 diff hist +146 Math 9A →Concepts
- 17:37, 23 November 2015 diff hist +7,723 N Implicit Differentiation Created page with " == Background == So far, you may only have differentiated functions written in the form <math style="vertical-align: -5px">y=f(x)</math>. But some functions are better descr..."
- 17:30, 23 November 2015 diff hist 0 N File:Tangent line and curve.png current
- 17:30, 23 November 2015 diff hist 0 N File:Curve.png current
- 17:29, 23 November 2015 diff hist 0 N File:Lower semicircle.png current
- 17:29, 23 November 2015 diff hist 0 N File:Upper semicircle.png current
- 12:23, 21 November 2015 diff hist +1,076 N Hyperbola Created page with "<div class="noautonum">__TOC__</div> ==Definition== Similar to an ellipse, a hyperbola has two foci and is defined as all the points whose distance from the foci is fixed. A..." current
- 12:23, 21 November 2015 diff hist +39 Math 5
- 12:06, 21 November 2015 diff hist +500 N Circle Created page with "<div class="noautonum">__TOC__</div> ==Definition== A circle is the set of points that are a fixed distance r, called the radius, from a fixed point (x, y), called the center..." current
- 12:06, 21 November 2015 diff hist +34 Math 5
- 12:02, 21 November 2015 diff hist +1,880 N Ellipse Created page with "<div class="noautonum">__TOC__</div> ==Definition== Similar to a parabola, an ellipse is defined by some fixed distance from a pair of points, called foci. The ellipse is the..." current
- 12:01, 21 November 2015 diff hist +36 Math 5
- 23:45, 20 November 2015 diff hist 0 Parabola current
- 23:33, 20 November 2015 diff hist +1,214 N Parabola Created page with "<div class="noautonum">__TOC__</div> ==Definition== A parabola is the collection of points that are equidistant from a line, called the directrix, and a point not on the line..."
- 23:33, 20 November 2015 diff hist +38 Math 5 →Concepts
- 23:18, 15 November 2015 diff hist +2,459 N Section 1.12 Created page with "'''8.''' Let <math>L: V \to W</math> be a linear map.<br /> <br /> (b) Show that if <math>x_1,x_2,...,x_k</math> are linearly dependent, then <math>L(x_1),L(x_2),...,L(x_k)</m..." current
- 23:17, 15 November 2015 diff hist +5,407 N Section 1.11 Created page with "'''7.''' Show that two 2-dimensional subspaces of a 3-dimensional subspace must have nontrivial intersection.<br /> <br /> {| class="mw-collapsible mw-collapsed" style = "text..." current
- 23:17, 15 November 2015 diff hist +4,626 N Section 1.10 Created page with "'''3.''' Let <math>L: V \to W</math> be a linear map and <math>N \subset W</math> a subspace. Show that: <math>L^{-1}(N) = \{ x\in V: L(x) \in N\}</math> is a subspace of <ma..." current
- 23:16, 15 November 2015 diff hist +5,204 N Section 1.8 Created page with "'''1.''' Let <math>L, K: V \to V</math> be linear maps between finite-dimensional vector spaces that satisfy <math>L \circ K = 0</math>. Is it true that <math>K \circ L = 0</m..." current
- 23:15, 15 November 2015 diff hist +4,664 N Section 1.7 Created page with "'''3.''' Find the matrix representation for <math> D^2 + 2D+1_{P_3}: P_3 \to P_3</math> with respect to the basis <math>1, t, t^2, t^3</math>.<br /> <br /> {| class="mw-colla..." current
- 23:15, 15 November 2015 diff hist +8,184 N Section 1.4 Created page with "'''1.''' Find a subset <math>C \subset \mathbb{F}^2</math> that is closed under scalar multiplication but not under addition of vectors.<br /> <br /> {| class="mw-collapsible..." current
- 23:14, 15 November 2015 diff hist +16,219 N Vector Space Problems Created page with "'''Exercise''' Show that <math>\{1+i,1-i \}</math> form a linearly independent set of vectors in <math>\mathbb{C}</math>, viewed as a vector space over <math>\mathbb{R}</math>..." current
- 23:13, 15 November 2015 diff hist +287 N Math 131 Created page with "The following are a collection of problems from Peter Peterson's text "Linear Algebra." Section 1.4 Section 1.7 Section 1.8 Section 1.10 Section 1.11..." current
- 18:23, 14 November 2015 diff hist +72 Vectors current
- 18:22, 14 November 2015 diff hist +3,357 N Vectors Created page with "<div class="noautonum">__TOC__</div> == Vectors== Vectors can be thought of as arrows in the plane, or rays of finite length. We add them together by first following one arro..."
- 18:21, 14 November 2015 diff hist +31 Math 5 →Concepts
- 17:40, 14 November 2015 diff hist +786 N Double Angle and Half Angle Formulas Created page with "<div class="noautonum">__TOC__</div> == Recovering the Double Angle Formulas== Using the sum formula and difference formulas for Sine and Cosine we can observe the following..." current
- 17:37, 14 November 2015 diff hist +90 Math 5 →Concepts
- 17:23, 14 November 2015 diff hist +698 N Sum and Difference Formulas Created page with "<div class="noautonum">__TOC__</div> == Sum and Difference Formula for Cosine== Given two angles <math> \alpha \text{ and } \beta</math> we have the following formulas: ::<m..." current
- 17:21, 14 November 2015 diff hist +71 Math 5 →Concepts
- 17:09, 14 November 2015 diff hist +822 N Trigonometric Identities Created page with "<div class="noautonum">__TOC__</div> == List of identities== Given two functions f and g, we say f = g if f(x) = g(x) for all every x in the domain of both f and g. Quotien..." current
- 17:09, 14 November 2015 diff hist +65 Math 5 →Concepts
- 17:56, 8 November 2015 diff hist +1 Math 4 current
- 17:55, 8 November 2015 diff hist +70 Math 4
- 17:51, 8 November 2015 diff hist +25 Math 4 →Concepts
- 16:29, 7 November 2015 diff hist +1,900 N Inverse Trig Functions 1 Created page with "<div class="noautonum">__TOC__</div> == Review of Trig Functions== Before discussing inverse trig functions we will recall how Sine, Cosine, and Tangent are defined. All thre..." current
- 16:28, 7 November 2015 diff hist +74 Math 5 →Concepts
- 23:21, 3 November 2015 diff hist +1 Properties of Trigonometric Functions →Periods of trigonometric functions current
