User contributions for CarrieGeng
16 April 2015
- 06:0306:03, 16 April 2015 diff hist +101 Science:Math Exam Resources/Courses/MATH152/April 2011/Question B 02 (a) No edit summary
- 06:0206:02, 16 April 2015 diff hist +101 Science:Math Exam Resources/Courses/MATH152/April 2011/Question B 05 (c) No edit summary
- 06:0106:01, 16 April 2015 diff hist −32 Science:Math Exam Resources/Courses/MATH152/April 2010/Question B 02 (b) No edit summary
- 06:0006:00, 16 April 2015 diff hist +83 Science:Math Exam Resources/Courses/MATH152/April 2010/Question B 02 (b) No edit summary
- 05:5805:58, 16 April 2015 diff hist +68 Science:Math Exam Resources/Courses/MATH152/April 2010/Question A 06 No edit summary current
- 05:5705:57, 16 April 2015 diff hist +70 Science:Math Exam Resources/Courses/MATH152/April 2011/Question A 05 No edit summary current
- 05:5305:53, 16 April 2015 diff hist +58 Science:Math Exam Resources/Courses/MATH104/December 2010/Question 01 (e) No edit summary
- 05:4905:49, 16 April 2015 diff hist +34 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (b) No edit summary current
- 05:4705:47, 16 April 2015 diff hist +40 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (a) No edit summary
- 05:4505:45, 16 April 2015 diff hist +44 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 05 No edit summary
- 05:4405:44, 16 April 2015 diff hist +40 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 03 No edit summary
- 05:4205:42, 16 April 2015 diff hist +44 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 02 No edit summary
- 05:4105:41, 16 April 2015 diff hist +97 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 01 (j) No edit summary
- 05:3805:38, 16 April 2015 diff hist +95 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 01 (e) No edit summary current
- 05:3505:35, 16 April 2015 diff hist +99 Science:Math Exam Resources/Courses/MATH257/December 2011/Question 03 (a) No edit summary
14 April 2015
- 06:1006:10, 14 April 2015 diff hist 0 Science:Math Exam Resources/Courses/MATH257/December 2011/Question 01 No edit summary current
- 06:1006:10, 14 April 2015 diff hist +96 Science:Math Exam Resources/Courses/MATH257/December 2011/Question 01 No edit summary
- 06:0306:03, 14 April 2015 diff hist +8 Science:Math Exam Resources/Courses/MATH257/December 2011/Question 02 (b) No edit summary current
- 06:0106:01, 14 April 2015 diff hist 0 Science:Math Exam Resources/Courses/MATH257/December 2011/Question 02 (b) No edit summary
- 05:5705:57, 14 April 2015 diff hist +96 Science:Math Exam Resources/Courses/MATH257/December 2011/Question 02 (b) No edit summary
- 05:5605:56, 14 April 2015 diff hist −98 Science:Math Exam Resources/Courses/MATH257/December 2011/Question 02 (b)/Statement No edit summary current
- 05:3605:36, 14 April 2015 diff hist +98 Science:Math Exam Resources/Courses/MATH257/December 2011/Question 02 (b)/Statement No edit summary
12 April 2015
- 07:5407:54, 12 April 2015 diff hist +160 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 01 (h)/Solution 1 No edit summary
- 07:5307:53, 12 April 2015 diff hist +475 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 01 (f)/Solution 1 Created page with " To use the integral test, we need to compute <math>\begin{align} \int_2^{\infty}\frac{1}{x(\ln x)^p} dx\end{align}</math> Let <math>u=\ln x</math>, then <math>du=\frac{1}{x..."
8 April 2015
- 22:3122:31, 8 April 2015 diff hist −6 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (b)/Solution 1 No edit summary
- 22:3022:30, 8 April 2015 diff hist +1,082 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (b)/Solution 1 Created page with "Derive the formula in (a): <math>\begin{align} \sum_{n=0}^{\infty}n^2 x^{n-1} &=&\frac{d}{dx}\sum_{n=0}^{\infty} nx^n \\ &=&\frac{d}{dx}\left(\frac{x}{(1-x)^2}\right) \\ &=&..."
- 22:2922:29, 8 April 2015 diff hist +90 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (b)/Hint 2 Created page with " Use the ratio test for the interval of convergence. Check the boundaries of the interval." current
- 22:2922:29, 8 April 2015 diff hist −1,024 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (b)/Hint 1 Replaced content with " Use the formula in (a). Check the derivative of it." current
- 22:2822:28, 8 April 2015 diff hist −6 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (b)/Hint 1 No edit summary
- 22:2722:27, 8 April 2015 diff hist +1,082 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (b)/Hint 1 Created page with "Derive the formula in (a): <math>\begin{align} \sum_{n=0}^{\infty}n^2 x^{n-1} &=&\frac{d}{dx}\sum_{n=0}^{\infty} nx^n \\ &=&\frac{d}{dx}\left(\frac{x}{(1-x)^2}\right) \\ &=&..."
- 22:2622:26, 8 April 2015 diff hist +400 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (a)/Solution 1 Created page with "By geometric series, we know <math>\begin{align} \frac{1}{1-x}=\sum_{n=0}^{\infty}x^n.\end{align}</math> Derive both side: <math>\begin{align} \frac{1}{(1-x)^2}=\frac{d}{dx..."
- 22:2522:25, 8 April 2015 diff hist +42 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (a)/Hint 2 Created page with "How does the derivative affect the series?" current
- 22:2522:25, 8 April 2015 diff hist +27 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (a)/Hint 1 Created page with " Consider geometric series." current
- 22:2222:22, 8 April 2015 diff hist +1,832 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 08/Solution 1 Created page with " By the Taylor series formula, <math>\begin{align} f(x)=\sum_{n=0}^{\infty}c_n(x-2)^n\end{align}</math> where <math>\begin{align} c_0=f(2) \quad \text{and}\quad c_n=\frac{f..."
- 22:0922:09, 8 April 2015 diff hist +102 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 08/Hint 3 Created page with "(Interval of convergence) What test do we need to use for convergence? Check also the end point cases."
- 22:0922:09, 8 April 2015 diff hist +123 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 08/Hint 2 Created page with " Find the first few derivative, general form for nth derivative. Keep track of contributions towards constant and the sign." current
- 22:0222:02, 8 April 2015 diff hist +88 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 08/Hint 1 Created page with " What is the Taylor series formula for some function <math>f</math> at <math>x=a</math>?" current
- 22:0022:00, 8 April 2015 diff hist +95 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 07 (b)/Hint 1 Created page with "Evaluate <math>\cos (n\pi)</math> for the first few values for <math>n</math> to see a pattern." current
- 22:0022:00, 8 April 2015 diff hist +499 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 07 (b)/Solution 1 Created page with " First, since <math>\cos(\pi)=-1</math>, <math>\cos(2\pi)=1</math>, <math>\cos(3\pi)=-1</math>, <math>\cdots</math>, <math>\cos(n\pi)=(-1)^n</math>. Thus, the given series is..."
- 20:3920:39, 8 April 2015 diff hist +719 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 07 (a)/Solution 1 Created page with "Note that <math>\frac{1}{\sqrt{n^2+1}}</math> is similar to <math>\frac{1}{\sqrt{n^2}}=\frac{1}{n}</math> for large <math>n</math>. So, we expect that the series diverges. Si..."
- 20:3620:36, 8 April 2015 diff hist +60 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 07 (a)/Hint 2 Created page with " Compare with <math>\frac{1}{\sqrt{n^2}}=\frac{1}{n}</math>."
- 20:3620:36, 8 April 2015 diff hist +169 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 07 (a)/Hint 1 Created page with " Consider a function whose behavior is similar with <math>\frac{1}{\sqrt{x^2+1}}</math>. From that function, analogize the convergence or divergence of the given series."
- 20:3420:34, 8 April 2015 diff hist +931 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 06/Solution 1 Created page with "By the separation of variables, <math>\begin{align} &x\frac{dy}{dx}&=y^2-y \\ &\int \frac{1}{y^2-y} dy &=\int \frac{1}{x} dx \\ &\int \frac{1}{y(y-1)}&=\ln|x|+C\end{align}<..."
- 20:3420:34, 8 April 2015 diff hist +92 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 06/Hint 3 Created page with " Keep track of the absolute value and determine the solution which satisfy the initial data." current
- 20:3320:33, 8 April 2015 diff hist +83 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 06/Hint 1 Created page with " How can we solve a differential equation? Think about the separation of variables." current
- 20:3320:33, 8 April 2015 diff hist +51 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 06/Hint 2 Created page with "Use partial fraction when you compute the integral." current
- 20:3120:31, 8 April 2015 diff hist +16 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 05/Solution 1 No edit summary
- 20:3120:31, 8 April 2015 diff hist +1,712 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 05/Solution 1 Created page with "First, the given region is the following: MISSING FIGURE HERE: 6cm picture5. jpg By the formula for the centroid, we have <math>\begin{align} \bar{x}=\frac{1}{A}\int_0^{\f..."
- 20:3020:30, 8 April 2015 diff hist +189 N Science:Math Exam Resources/Courses/MATH101/April 2014/Question 05/Hint 1 Created page with " Use the formula for the centroid: <math>\begin{align} \bar{x}=\frac{1}{A}\int_a^b x(f(x)-g(x))dx,\quad\text{and}\quad \bar{y}=\frac{1}{2A}\int_a^b [f(x)]^2-[g(x)]^2 dx. \end..."
- 20:2920:29, 8 April 2015 diff hist +17 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 04/Solution 1 No edit summary