User contributions for Toanle95
6 April 2015
- 20:1020:10, 6 April 2015 diff hist +2 Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 03/Solution 1 No edit summary current
- 20:1020:10, 6 April 2015 diff hist +49 Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 03/Solution 1 No edit summary
- 20:0820:08, 6 April 2015 diff hist +268 N File:December 2014 Math 102 Final Exam Question C3-2.png User created page with UploadWizard current
- 20:0520:05, 6 April 2015 diff hist +1,852 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 03/Solution 1 Created page with "As indicated in the hint, we define <math>\theta</math> as the angle to the top of the screen* and <math>\phi</math> as the angle to the bottom of the screen. Then <math>\tan(..."
- 20:0420:04, 6 April 2015 diff hist +113 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 03/Hint 1 Created page with "Maximize the difference of the two angles <math>\theta</math> and <math>\phi</math> with implicit differentiation" current
- 20:0420:04, 6 April 2015 diff hist +582 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 03/Statement Created page with "thumb|Stanley Park At the outdoor summer movie at Stanley Park, the bottom of the screen is 2 meters above your eye..." current
- 20:0420:04, 6 April 2015 diff hist +271 N File:December 2014 Math 102 Final Exam Question C3.png User created page with UploadWizard current
- 20:0120:01, 6 April 2015 diff hist +636 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (d)/Solution 1 Created page with "Same as in C2(a), to solve the steady states, we just need to solve the following equation <math>c(rc^2-P_mc+k^2rc)=0,</math> Obviously <math>c=0</math> is one of the steady s..."
- 20:0120:01, 6 April 2015 diff hist +94 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (d)/Hint 3 Created page with "The quadratic equation <math>ax^2+bx+c</math> has one solution when <math>b^2 - 4ac = 0</math>" current
- 20:0120:01, 6 April 2015 diff hist +106 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (d)/Hint 2 Created page with "In part a), we determine the value of the steady state by setting <math>c(rc^2-P_mc+k^2r)</math> equals 0." current
- 20:0020:00, 6 April 2015 diff hist +85 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (d)/Hint 1 Created page with "How to solve the steady state? When does a quadratic equation have only one solution?" current
- 20:0020:00, 6 April 2015 diff hist +601 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (d)/Statement Created page with "The graphs to the right show two functions, thumb|Graphs| 400px <math>P(c) = P_m \frac{c^2}{k^2+c^2}, \quad D(c) =..." current
- 19:5919:59, 6 April 2015 diff hist +200 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (c)/Solution 1 Created page with "If <math>c(0)=8</math> then it falls in the region <math>(5,20)</math> and <math>P(c)-D(c)>0</math>. So <math>c</math> would increase with time and finally approach the steady..."
- 19:5919:59, 6 April 2015 diff hist +144 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (c)/Hint 1 Created page with "Is the derivative <math>dc/dt</math> positive or negative at <math>c(0)=8</math>? Will the function increase or decrease after <math>t=0</math>?" current
- 19:5919:59, 6 April 2015 diff hist +6 Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (c)/Statement No edit summary current
- 19:5819:58, 6 April 2015 diff hist +529 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (c)/Statement Created page with "The graphs to the right show two functions, thumb|Graphs <math>P(c) = P_m \frac{c^2}{k^2+c^2}, \quad D(c) = rc</ma..."
- 19:5719:57, 6 April 2015 diff hist +818 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (b)/Solution 1 Created page with "To determine the stability of each steady state, we just need to find the increasing and decreasing regions. As <math>c</math> represents the concentration of a substance, we..." current
- 19:5619:56, 6 April 2015 diff hist +475 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (b)/Hint 1 Created page with "A steady state is stable if states that are initially close enough to that steady state will get closer to it with time. A steady state is unstable, if states that are initial..." current
- 19:5619:56, 6 April 2015 diff hist +544 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (b)/Statement Created page with "The graphs to the right show two functions, thumb|Graphs| 400px <math>P(c) = P_m \frac{c^2}{k^2+c^2}, \quad D(c) =..." current
- 19:5519:55, 6 April 2015 diff hist +8 Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (a)/Solution 1 No edit summary
- 19:5219:52, 6 April 2015 diff hist −13 Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (a)/Solution 1 No edit summary
- 19:5219:52, 6 April 2015 diff hist +491 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (a)/Solution 1 Created page with "By the definition of steady state, we look for the value of <math>c</math> such that <math>\frac{dc}{dt}=0, \quad \text{or } P(c)-D(c)=0.</math> Thus we need to solve <math>\..."
- 19:5119:51, 6 April 2015 diff hist +158 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (a)/Hint 1 Created page with "A Steady state is a state in which a system is not changing. So it is calculated by setting <math>\frac{dc}{dt}=0</math> and find the solution <math>c</math>." current
- 19:5119:51, 6 April 2015 diff hist +1 Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (a)/Statement No edit summary current
- 19:5119:51, 6 April 2015 diff hist +7 Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (a)/Statement No edit summary
- 19:5019:50, 6 April 2015 diff hist −1 Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (a)/Statement No edit summary
- 19:4919:49, 6 April 2015 diff hist +486 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 02 (a)/Statement Created page with "The graphs to the right show two functions, <math>P(c) = P_m \frac{c^2}{k^2+c^2}, \quad D(c) = rc</math> where <math>P_m=5</math>, <math>k=10</math> and <math>r=1/5</math>. S..."
- 19:4919:49, 6 April 2015 diff hist +265 N File:December 2014 Math 102 Final Exam Question C2.png User created page with UploadWizard current
- 19:4719:47, 6 April 2015 diff hist +685 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 01/Solution 1 Created page with "Let <math>x=\cot(\theta)</math>, we can rewrite it as <math>x=\frac{\cos(\theta)}{\sin(\theta)},</math> With implicit differentiation we take the derivative of above expressio..." current
- 19:4619:46, 6 April 2015 diff hist +265 N File:December 2014 Math 102 Final Exam Question C1.png User created page with UploadWizard current
- 19:4419:44, 6 April 2015 diff hist +278 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 01/Hint 1 Created page with "Rewrite the expression as <math>x=\cot(\theta)=\frac{\cos(\theta)}{\sin(\theta)}</math> and use quotient rule <math>\Big(\frac{g(x)}{h(x)}\Big)'=\frac{g'(x)h(x)-g(x)h'(x)}{h^2..." current
- 19:4319:43, 6 April 2015 diff hist +158 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question C 01/Statement Created page with "Use implicit differentiation to calculate the derivative of <math>\theta(x)=\text{arccot}(x)</math>. Recall that <math>\cot(x)=\frac{\cos(x)}{\sin(x)}</math>." current
- 19:4219:42, 6 April 2015 diff hist +205 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 07/Hint 2 Created page with "When the runner crosses the finish line, <math>x'=0</math> as the elliptical track is perpendicular to the <math>x</math>-axis at that point. So there is no <math>x</math> com..." current
- 19:4119:41, 6 April 2015 diff hist +1,309 Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 07/Solution 1 No edit summary
- 19:4119:41, 6 April 2015 diff hist +265 N File:December 2014 Math 102 Final Exam Question B7.png User created page with UploadWizard current
- 19:3919:39, 6 April 2015 diff hist +205 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 07/Solution 1 Created page with "When the runner crosses the finish line, <math>x'=0</math> as the elliptical track is perpendicular to the <math>x</math>-axis at that point. So there is no <math>x</math> com..."
- 19:3919:39, 6 April 2015 diff hist +370 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 07/Hint 1 Created page with "Set the angle between the line which connects the runner and the origin and the positive x-axis to be <math>\theta</math>, then if the runner is at location <math>(x,y)</math>..." current
- 19:3819:38, 6 April 2015 diff hist +369 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 07/Statement Created page with "A runner on an elliptical track described by the equation <math>x^2 + \dfrac{y^2}{4} =900</math> runs at a constant speed <math>v</math> where <math>x</math> and <math>y</math..." current
- 19:3719:37, 6 April 2015 diff hist +417 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 06/Solution 1 Created page with "From the definition of linear approximation we know that, for <math>x</math> close to <math>a</math>, we can approximation function value <math>f(x)</math> by the following fo..."
- 19:3719:37, 6 April 2015 diff hist +168 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 06/Hint 1 Created page with "For <math>x</math> close to <math>a</math>, The linear approximation <math>L(x)</math> to <math>f(x)</math> has form <math>f(x)\thickapprox L(x)=f(a)+f'(a)(x-a).</math>" current
- 19:3719:37, 6 April 2015 diff hist +96 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 06/Statement Created page with "Use linear approximation to estimate <math>\ln(0. 95)</math>. Recall that <math>\ln(1)=0</math>." current
- 19:3619:36, 6 April 2015 diff hist +372 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 05/Solution 1 Created page with "To approximate <math>y(1/4)</math>, we use the Euler’s method <math>y_{n+1}=y_n+\Delta tf(y_n).</math> with a single step <math>\Delta t=1/4</math> and <math>n=0</math>, whe..." current
- 19:3619:36, 6 April 2015 diff hist +170 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 05/Hint 1 Created page with "The Euler’s method has form <math>y_{n+1}=y_n+\Delta tf(y_n),</math> where <math>f(y)</math> is the derivative of <math>y</math>, i. e. <math>\frac{dy}{dt}=f(y)</math>." current
- 19:3519:35, 6 April 2015 diff hist +255 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 05/Statement Created page with "Consider the differential equation <math>\dfrac{dy}{dt} =2(1-y)</math> with the initial condition <math>y(0)=2</math>. Using Euler’s method with a single step of size <math>..." current
- 19:3519:35, 6 April 2015 diff hist −6 Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 04/Solution 1 No edit summary
- 19:3419:34, 6 April 2015 diff hist +1,082 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 04/Solution 1 Created page with "The general expression of a cosine function is <math>T(t)=A+B\cos(\omega t+\varphi).</math> Suppose <math>A</math>, <math>B</math> are both positive. Here the lowest temperatu..."
- 19:3319:33, 6 April 2015 diff hist +50 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 04/Hint 1 Created page with "How to stretch or shift a sine or cosine function?"
- 19:3319:33, 6 April 2015 diff hist +415 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 04/Statement Created page with "The daily temperature in Vancouver during the month of March varies from an average low of 2 <math>^{\circ}</math> C to an average high of 10 <math>^{\circ}</math> C. It is co..."
- 19:3219:32, 6 April 2015 diff hist +438 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 03/Solution 1 Created page with "In this problem we know the point is at <math>a=\frac{\pi}{4}</math> and the function value <math>f(a)=f(\frac{\pi}{4})=\tan(\frac{\pi}{4})=1</math>. To calculate <math>f'(\fr..." current
- 19:3119:31, 6 April 2015 diff hist +120 N Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 03/Hint 1 Created page with "The equation of the tangent line to function <math>f(x)</math> at <math>x=a</math> is <math>L(x)=f(a)+f'(a)(x-a).</math>" current