User contributions for ThomasWong
9 April 2015
- 19:2519:25, 9 April 2015 diff hist −1 Science:Math Exam Resources/Courses/MATH101/April 2014/Question 09 (b)/Solution 1 No edit summary
5 March 2015
- 00:4200:42, 5 March 2015 diff hist +135 N Science:Math Exam Resources/Courses/MATH110/April 2014/Question 01 (a)/Statement Created page with "If <math>f</math> is defined on the closed interval <math>[-1,1]</math>, then <math>f</math> attains a global maximum on that interval." current
17 November 2014
- 06:5706:57, 17 November 2014 diff hist +16 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 05 (a)/Solution 1 No edit summary
- 06:5606:56, 17 November 2014 diff hist +4 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 05 (a)/Solution 1 No edit summary
- 06:5506:55, 17 November 2014 diff hist −8 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 05 (a)/Solution 1 No edit summary
- 06:5406:54, 17 November 2014 diff hist +2,586 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 05 (a)/Solution 1 No edit summary
- 00:1300:13, 17 November 2014 diff hist +669 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 01 (c)/Solution 1 No edit summary
16 November 2014
- 06:3706:37, 16 November 2014 diff hist +534 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 10 (a)/Solution 1 Created page with "We have <math>4</math> slots to fill and <math>7</math> people to fill them. So that means, we have <math>7</math> choices for the first slot, <math>6</math> for the second, <..."
- 06:3706:37, 16 November 2014 diff hist +491 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 10 (b)/Solution 1 Created page with "When selecting courses, the order does not matter. So I am really interested in a combination here. I have want to select <math>5</math> of the <math>9</math> available course..."
- 06:3606:36, 16 November 2014 diff hist +41 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 10 (b)/Statement No edit summary
- 06:3606:36, 16 November 2014 diff hist +238 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 10 (b)/Statement Created page with "There are $9$ courses I want to take next term. All $9$ courses are offered during the same $5$ time slots. How many ways do I have to fill those $5$ time slots? \emph{For th..."
- 06:3506:35, 16 November 2014 diff hist +259 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 10 (a)/Statement Created page with "How many ways can <math>7</math> graduate students be assigned to teach the <math>4</math> sections of MATH110 next year if each graduate student can be assigned to at most on..."
- 06:3406:34, 16 November 2014 diff hist −4 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 09/Solution 1 No edit summary
- 06:3306:33, 16 November 2014 diff hist +1,285 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 09/Solution 1 Created page with "We first check that the point <math>(0,\pi)</math> is on the line: <math>\begin{aligned} \sin(0+\pi) &= 0 \cdot \pi\\ \sin(\pi) &=0\\ 0&=0\end{aligned}</math> Check. The poi..."
- 06:3006:30, 16 November 2014 diff hist +152 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 09/Statement Created page with "Find the derivative of <math>y</math> with respect to <math>x</math> at the point <math>P = (0,\pi)</math> along the curve: <math>\sin(x+y) = xy</math>"
- 06:2906:29, 16 November 2014 diff hist −12 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 08/Solution 1 No edit summary current
- 06:2806:28, 16 November 2014 diff hist +987 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 08/Solution 1 Created page with "The condition for <math>f</math> to be continuous is <math>\begin{aligned} \lim_{x\rightarrow t^-} f(x) &= \lim_{x\rightarrow t^+} f(x)\\ e^{-t}&=2(t+1)\end{aligned}</math> ..."
- 06:2806:28, 16 November 2014 diff hist +341 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 08/Statement Created page with "Let <math>f(x) = \left\{ \begin{array}{lr} e^{-x} & \text{if}\quad x < t\\ 2(x+1) & \text{if} \quad x \geq t \end{array} \right.</math> Explain why ..."
- 06:2606:26, 16 November 2014 diff hist +1,344 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 07/Solution 1 Created page with "<ul> <li><p>We can solve this problem ‘normally’ by using product and chain rule or by using logarithmic differentiation.</p> <p><math>\begin{align} f'(x)&=7(x^2+1)^6(x^4+..."
- 06:2506:25, 16 November 2014 diff hist +133 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 07/Statement Created page with "Find the derivative of the function <math>f(x)=(x^2+1)^7(x^4+2)^5(x^6+3)^3(x^8+4).</math> (There is no need to simplify your answer.)" current
- 06:2406:24, 16 November 2014 diff hist +388 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (c)/Solution 1 Created page with "Recall that <math>f'(x) = \left(3x^2 + 4x + 1\right)\cdot e^{x^3 + 2x^2 + x - 3}.</math> From part a), we know that <math>e^{x^3 + 2x^2 + x - 3}\neq 0</math>. So that means ..."
- 06:2306:23, 16 November 2014 diff hist +191 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (c)/Statement Created page with "Consider the function: <math>f(x) = \dfrac{e^{\left(x^3\right)}e^{\left(2x^2\right)}e^{x}}{e^3}.</math> How many solutions are there to the equation <math>f'(x)=0</math>? Just..."
- 06:2206:22, 16 November 2014 diff hist −8 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (b)/Solution 1 No edit summary
- 06:2106:21, 16 November 2014 diff hist +1,209 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (b)/Solution 1 No edit summary
- 06:2006:20, 16 November 2014 diff hist −388 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (b)/Solution 1 Blanked the page
- 06:1706:17, 16 November 2014 diff hist −46 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (b)/Statement No edit summary
- 06:1606:16, 16 November 2014 diff hist +388 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (b)/Solution 1 Created page with "Recall that <math>f'(x) = \left(3x^2 + 4x + 1\right)\cdot e^{x^3 + 2x^2 + x - 3}.</math> From part a), we know that <math>e^{x^3 + 2x^2 + x - 3}\neq 0</math>. So that means ..."
- 06:1506:15, 16 November 2014 diff hist +191 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (b)/Statement Created page with "Consider the function: <math>f(x) = \dfrac{e^{\left(x^3\right)}e^{\left(2x^2\right)}e^{x}}{e^3}.</math> How many solutions are there to the equation <math>f'(x)=0</math>? Just..."
- 06:1406:14, 16 November 2014 diff hist +546 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (a)/Solution 1 Created page with "We first simplify using the exponential rules to get <math>f(x) = e^{x^3 + 2x^2 + x - 3}.</math> Then we can solve for <math>f(x) = 0</math>. <math>\begin{align} e^{x^3 + 2x^..." current
- 06:1306:13, 16 November 2014 diff hist +190 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (a)/Statement Created page with "Consider the function: <math>f(x) = \dfrac{e^{\left(x^3\right)}e^{\left(2x^2\right)}e^{x}}{e^3}.</math> How many solutions are there to the equation <math>f(x)=0</math>? Justi..."
15 November 2014
- 01:2701:27, 15 November 2014 diff hist +1,446 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 05 (b)/Solution 1 Created page with "To find the equation of the tangent line, we need to find the slope via the derivative. We can either apply the quotient rule or the power rule (by recognising <math>y = \tan(..."
- 01:2601:26, 15 November 2014 diff hist +123 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 05 (b)/Statement Created page with "Find the equation of the line tangent to the curve <math>y=\dfrac{\cos x}{\sin x}</math> at <math>x=\dfrac{5\pi}{3}</math>." current
- 01:2301:23, 15 November 2014 diff hist +192 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 05 (a)/Solution 1 Created page with "* <math>\sin\left(\frac{5\pi}{3}\right) = -\frac{\sqrt{3}}{2}.</math> * <math>\cos\left(-\frac{\pi}{3}\right) = \frac{1}{2}.</math> * <math>\tan\left(\frac{11\pi}{3}\right) = ..."
- 01:2201:22, 15 November 2014 diff hist +179 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 05 (a)/Statement Created page with "Evaluate the following three quantities: <math>\sin\left(\frac{5\pi}{3}\right)</math>, <math>\cos\left(-\frac{\pi}{3}\right)</math>, <math>\tan\left(\frac{11\pi}{3}\right)</ma..." current
- 01:2001:20, 15 November 2014 diff hist +425 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 04 (c)/Solution 1 Created page with "We want to apply the chain rule. Set <math>u = \sqrt{x}-1</math>. <math>\begin{align} g(u) &= \sqrt{u}-1 & g'(u) &= \frac{1}{2\sqrt{u}}\\ u(x) &= \sqrt{x}-1 & u'(x) &= \frac{..." current
- 01:1901:19, 15 November 2014 diff hist +111 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 04 (c)/Statement Created page with "Let <math>f(x)=\sqrt{x}-1</math> and <math>g(x)=(f\circ f)(x)</math>. Find the derivative of <math>g(x)</math>." current
- 01:1801:18, 15 November 2014 diff hist +459 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 04 (b)/Solution 1 Created page with "Looking at the outside function, we want to find <math>\sqrt{x}-1\geq 0</math> for <math>\sqrt{\sqrt{x}-1}</math> to be defined. So we want <math>\sqrt{x} \geq 1</math>. Look..." current
- 01:1701:17, 15 November 2014 diff hist −1 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 04 (b)/Statement No edit summary current
- 01:1601:16, 15 November 2014 diff hist +111 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 04 (b)/Statement Created page with "Let <math>f(x)=\sqrt{x}-1</math> and <math>g(x)=(f\circ f)(x)</math>. Find the derivative of <math>g(x)</math>."
- 01:1501:15, 15 November 2014 diff hist +144 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 04 (a)/Solution 1 Created page with "We simply substitute: <math>\begin{align} g(x) &= (f\circ f)(x)\\ &= f(f(x))\\ &= f(\sqrt{x}-1)\\ g(x)&= \sqrt{\sqrt{x}-1}-1.\end{align}</math>" current
- 01:1401:14, 15 November 2014 diff hist +212 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 04 (a)/Statement Created page with "Let <math>f(x)=\sqrt{x}-1</math> and <math>g(x)=(f\circ f)(x)</math>. Find a formula for <math>g(x)</math> in terms of <math>x</math> (in other words, your formula should not ..." current
- 01:1001:10, 15 November 2014 diff hist +1,383 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 03 (b)/Solution 1 Created page with "<span>'''Parts b and c combined:'''</span> (These are all the rules I can think of). <ul> <li><p>Addition rule:</p> <p><math>\begin{align} f(x) &= \frac{1}{2}x^6 + \frac{1}{2..." current
- 01:0901:09, 15 November 2014 diff hist +273 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 03 (b)/Statement Created page with "Rewrite <math>f(x)</math> in such a way that you can differentiate it using a different rule than the Power Rule. Name the rule of differentiation which is applicable, and the..."
- 01:0801:08, 15 November 2014 diff hist +96 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 03 (a)/Solution 1 Created page with "Using the power rule with <math>n=6</math>. <math>\begin{align} f'(x)&= 6x^5.\end{align}</math>" current
- 01:0701:07, 15 November 2014 diff hist +44 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 03 (a)/Statement Created page with "What is the derivative of <math>f(x)</math>?"
- 01:0601:06, 15 November 2014 diff hist +1,713 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 02/Solution 1 Created page with "We first recognise that parallel means that the slopes must be equal. Rearranging the equation, we get: <math>\begin{align} x-2y &= 2\\ x-2 &= 2y\\ y&= \frac{x-2}{2}\\ y &= \..." current
- 00:5600:56, 15 November 2014 diff hist +503 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 01 (d)/Solution 1 Created page with "<span>'''False:'''</span> If <math>f(x)</math> is differentiable at <math>x=2</math>, then by the definition of derivative at a point, we have <math>\displaystyle f'(2) = \lim..."
- 00:5500:55, 15 November 2014 diff hist +406 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 01 (c)/Solution 1 Created page with "<span>'''False:'''</span> We can use the same function as the previous part (if we want) to show that we can have every point leading to <math>0</math> to be defined at <math>..."
- 00:5300:53, 15 November 2014 diff hist +323 N Science:Math Exam Resources/Courses/MATH110/December 2013/Question 01 (b)/Solution 1 Created page with "<span>'''False:'''</span> The easiest way to see this is to come up with a function where the limit exists but the function is not defined there. For example <math>f(x) = \fra..."
- 00:5200:52, 15 November 2014 diff hist 0 Science:Math Exam Resources/Courses/MATH110/December 2013/Question 01 (a) No edit summary