User contributions for ChinJeanChen
11 April 2015
- 19:2519:25, 11 April 2015 diff hist −47 Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (d)/Solution 1 No edit summary
- 19:2419:24, 11 April 2015 diff hist −62 Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (b)/Solution 1 No edit summary
- 19:2319:23, 11 April 2015 diff hist +88 Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (d)/Solution 1 No edit summary
- 19:2019:20, 11 April 2015 diff hist −28 Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (b)/Solution 1 No edit summary
- 19:1919:19, 11 April 2015 diff hist +124 Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (b)/Solution 1 No edit summary
- 06:2706:27, 11 April 2015 diff hist −1 Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (f)/Solution 1 No edit summary current
- 06:2706:27, 11 April 2015 diff hist −21 Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (f)/Solution 1 No edit summary
- 06:2506:25, 11 April 2015 diff hist +1,497 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (f)/Solution 1 Created page with "We know from part <math>a</math> that the critical point of <math>f</math> occurs at <math>x = 2</math>; hence the graph of the function will change from decreasing to the lef..."
- 06:2406:24, 11 April 2015 diff hist +265 N File:5fgraph.png User created page with UploadWizard current
- 06:2406:24, 11 April 2015 diff hist +355 N File:IMAG1942.jpg User created page with UploadWizard current
- 06:2406:24, 11 April 2015 diff hist +282 N File:IMAG1943.jpg User created page with UploadWizard current
- 06:2406:24, 11 April 2015 diff hist +323 N File:IMAG1941.jpg User created page with UploadWizard current
- 06:1906:19, 11 April 2015 diff hist +104 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (f)/Hint 1 Created page with "Combine all facts from <math>a</math> to <math>e</math> and see what they tell you about <math>f</math>." current
- 06:1906:19, 11 April 2015 diff hist +97 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (f)/Statement Created page with "Let <math>f(x) = \frac{e^x}{x^2}</math>. Sketch the graph of <math>f(x) = \frac{e^x}{x^2}</math>." current
- 06:1806:18, 11 April 2015 diff hist +71 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 06/Hint 3 Created page with "Additionally, Intermediate Value Theorem will be very very useful here." current
- 06:1806:18, 11 April 2015 diff hist +97 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 06/Hint 2 Created page with "Think about what the necessary and sufficient conditions are for there to be an inflection point." current
- 06:1806:18, 11 April 2015 diff hist +2,295 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 06/Solution 1 Created page with "The necessary condition for <math>f</math> to have an inflection point is that there exists a <math>c</math> in <math>(0, \infty)</math> so that <math>f''(c) = 0</math>. A suf..."
- 06:1706:17, 11 April 2015 diff hist +37 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 06/Hint 1 Created page with "Change the base of <math>\log</math>."
- 06:1706:17, 11 April 2015 diff hist +268 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 06/Statement Created page with "Let <math>f(x) = \frac{x^4}{12} - \frac{4(3^{-x})}{(\ln{3})^2} + \log_{(x+1)^2}(x+1)^{2014}</math> be a function defined on the interval <math>(0, \infty)</math>. Show that th..." current
- 06:1706:17, 11 April 2015 diff hist +2,286 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (e)/Solution 1 Created page with "We have already determined what the vertical asymptote is in part <math>a</math>, by seeing where <math>f</math> is undefined. To see the behaviour of <math>f</math> as it app..." current
- 06:1606:16, 11 April 2015 diff hist +49 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (e)/Hint 1 Created page with "How are limits and horizontal asymptotes related?" current
- 06:1606:16, 11 April 2015 diff hist +194 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (e)/Statement Created page with "Let <math>f(x) = \frac{e^x}{x^2}</math>. Find the horizontal asymptote and the vertical asymptote of <math>f(x)</math>. Note that <math>\lim_{x \rightarrow \infty} \frac{e^x}{..." current
- 06:1506:15, 11 April 2015 diff hist +1,242 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (d)/Solution 1 Created page with "Recall that when <math>f'' > 0</math>, <math>f</math> is concave up; likewise, when <math>f'' < 0</math>, <math>f</math> is concave down. So what we need to do is find the int..."
- 06:1506:15, 11 April 2015 diff hist +89 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (d)/Hint 1 Created page with "Find the intervals on which the second derivative <math>f''</math> exists and is nonzero." current
- 06:1506:15, 11 April 2015 diff hist +102 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (d)/Statement Created page with "Let <math>f(x) = \frac{e^x}{x^2}</math>. Find the intervals on which <math>f</math> is concave upward." current
- 06:1406:14, 11 April 2015 diff hist +581 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (c)/Solution 1 Created page with " Recall from part <math>a</math> that <math>f'(x) = \frac{e^x(x-2)}{x^3}</math>. We take the derivative of <math>f'</math> with respect to <math>x</math> using the quotient ru..." current
- 06:1406:14, 11 April 2015 diff hist +68 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (c)/Hint 1 Created page with "Take derivative of first derivative as found in part <math>a</math>." current
- 06:1306:13, 11 April 2015 diff hist +66 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (c)/Statement Created page with "Let <math>f(x) = \frac{e^x}{x^2}</math>. Find <math>f''(x)</math>." current
- 06:1306:13, 11 April 2015 diff hist −2 Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (b)/Solution 1 No edit summary
- 06:1206:12, 11 April 2015 diff hist +858 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (b)/Solution 1 Created page with "Remark first that <math>f</math> does not exist at <math>x = 0</math>; hence, we have three intervals on which <math>f'(x)</math> exists and is non–zero, namely <math>(-\inf..."
- 06:1206:12, 11 April 2015 diff hist +90 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (b)/Hint 1 Created page with "What are the intervals on which the derivative of <math>f</math> exists and is non–zero?"
- 06:1206:12, 11 April 2015 diff hist +112 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (b)/Statement Created page with "Let <math>f(x) = \frac{e^x}{x^2}</math>. Find the intervals on which <math>f</math> is increasing or decreasing." current
- 06:1106:11, 11 April 2015 diff hist +945 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (a)/Solution 1 Created page with "First, we determine <math>f'(x)</math>; rewrite <math>f(x) = e^xx^{-2}</math> and use product rule on <math>h(x) = e^x, g(x) = x^{-2}</math>: <math>\begin{align} f'(x) & = h(..."
- 06:1106:11, 11 April 2015 diff hist +48 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (a)/Hint 1 Created page with "How are critical points and derivatives related?" current
- 06:1106:11, 11 April 2015 diff hist +86 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 05 (a)/Statement Created page with "Let <math>f(x) = \frac{e^x}{x^2}</math>. Find the critical point of <math>f(x)</math>." current
- 06:1106:11, 11 April 2015 diff hist +74 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 04/Hint 2 Created page with "What does maximizing revenue mean mathematically, in terms of derivatives?" current
- 06:1006:10, 11 April 2015 diff hist +841 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 04/Solution 1 Created page with "We know that if we sell <math>x</math> bus tour tickets, we sell <math>y = 100 - x</math> train tour tickets. Let us now make the revenue function: <math>\begin{align} R & =..."
- 06:1006:10, 11 April 2015 diff hist +100 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 04/Hint 1 Created page with "If you sell <math>x</math> bus tour tickets, and there are a 100 passengers, what is <math>y</math>?" current
- 06:1006:10, 11 April 2015 diff hist +431 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 04/Statement Created page with "You are planning a city tour for a group of 100 tourists. If you can sell <math>x</math> bus tour tickets, you can offer them for <math>\$(30-x/4)</math> each. If you can sell..." current
- 06:0906:09, 11 April 2015 diff hist +528 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (c)/Solution 1 Created page with "From the above we know that when <math>q = 3</math>, by the relation give, <math>p = 2</math>. Now, we take that above relation and differentiate it with respect to time: <mat..."
- 06:0906:09, 11 April 2015 diff hist +125 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (c)/Hint 1 Created page with "What variable are you taking the derivative of demand with respect to (think about what unit of measurement is “months”)?" current
- 06:0906:09, 11 April 2015 diff hist +297 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (c)/Statement Created page with "The price <math>p</math> (in dollars) and the demand <math>q</math> for a product are related by the following demand equation: <math>p^3 + q + q^3 = 38</math> Suppose the pri..." current
- 06:0906:09, 11 April 2015 diff hist +2 Science:Math Exam Resources/Courses/MATH104/December 2014/Question 02/Solution 1 No edit summary
- 06:0806:08, 11 April 2015 diff hist +855 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (b)/Solution 1 Created page with "Substituting <math>q = 3</math> in the relation given, we obtain that <math>p^3 = 38 - 3 - 3^3 = 35 - 27 = 8 \Rightarrow p = 2</math>. Next, we determine the value of <math>q'..." current
- 06:0806:08, 11 April 2015 diff hist +51 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (b)/Hint 1 Created page with "The revenue function is given by <math>R=pq</math>." current
- 06:0806:08, 11 April 2015 diff hist +275 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (b)/Statement Created page with "The price <math>p</math> (in dollars) and the demand <math>q</math> for a product are related by the following demand equation: <math>p^3 + q + q^3 = 38</math> If the current..." current
- 06:0706:07, 11 April 2015 diff hist +31 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (a)/Hint 2 Created page with "Apply implicit differentiation." current
- 06:0706:07, 11 April 2015 diff hist +503 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (a)/Solution 1 Created page with "Recall that the price elasticity of a product is given by <math>e(p,q) = \frac{dq}{dp}\frac{p}{q}</math>, where <math>p</math> and <math>q</math>, are price and demand respect..."
- 06:0706:07, 11 April 2015 diff hist +60 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (a)/Hint 1 Created page with "What is the definition of the price elasticity of a product?"
- 06:0706:07, 11 April 2015 diff hist +259 N Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (a)/Statement Created page with "The price <math>p</math> (in dollars) and the demand <math>q</math> for a product are related by the following demand equation: <math>p^3 + q + q^3 = 38</math> Find the price..." current