User contributions for ChingWong
11 December 2018
- 14:1714:17, 11 December 2018 diff hist −39 Science:Math Exam Resources/Courses/MATH220/December 2009/Question 01 (a)/Solution 1 corrected the answer for f(C) current Tag: Visual edit
7 December 2018
- 09:5609:56, 7 December 2018 diff hist −75 Science:Math Exam Resources/Courses/MATH221/December 2008/Question 06 (a)/Solution 1 No edit summary current
6 December 2018
- 15:0715:07, 6 December 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH215/December 2013/Question 04 (a)/Statement No edit summary current
- 15:0715:07, 6 December 2018 diff hist +7 Science:Math Exam Resources/Courses/MATH215/December 2013/Question 04 (a)/Statement No edit summary
4 December 2018
- 12:4112:41, 4 December 2018 diff hist −1 m Science:Math Exam Resources/Courses/MATH102/December 2014/Question B 07/Solution 1 Changed some wordings to make the solution more clear. current Tag: Visual edit
29 November 2018
- 14:5514:55, 29 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 16 No edit summary
- 14:5414:54, 29 November 2018 diff hist +813 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 16/Solution 1 Created page with "Suppose <math display="inline">y=Ce^{rx}</math> is the curve of best fit for <math display="inline">(x_1,y_1),\dots,(x_n,y_n)</math>. Taking the logarithm, we have that <math..."
- 14:4914:49, 29 November 2018 diff hist +57 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 16/Hint 1 Created page with "Take logarithms on both side of the exponential relation." current
- 14:4814:48, 29 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 15 (b) No edit summary
- 14:4714:47, 29 November 2018 diff hist +979 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 15 (b)/Solution 1 Created page with "According to the Hint, let us compute the acceleration, which is the second derviative: <math display="block">h(t)=3+3\sin(\dfrac53t)</math> <math display="block">h'(t)=3\cos(..."
- 14:4214:42, 29 November 2018 diff hist +71 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 15 (b)/Hint 1 Created page with "The acceleration is the second derivative of the displacement (height)." current
- 14:4114:41, 29 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 15 (a) No edit summary
- 14:4014:40, 29 November 2018 diff hist +674 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 15 (a)/Solution 1 Created page with "By the Hint, <math display="block">\sin(\dfrac53t+2\pi)=\sin(\dfrac53t).</math> Factoring our <math display="inline">\dfrac53</math>, we have <math display="block">\sin(\dfrac..."
- 14:3614:36, 29 November 2018 diff hist +70 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 15 (a)/Hint 1 Created page with "The period of the sine function is <math display="inline">2\pi</math>."
- 14:3614:36, 29 November 2018 diff hist +1 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 14 (a)/Hint 1 No edit summary
- 14:3514:35, 29 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 14 (a) No edit summary
- 14:3514:35, 29 November 2018 diff hist +658 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 14 (a)/Solution 1 Created page with "Since <math display="block">V'(t)=\dfrac{100\pi}{15}(20-t),</math> we have, by the Hint, <math display="block">V(t)=-\dfrac{100\pi}{15}\dfrac{(20-t)^2}{2}+C,</math> where <mat..."
- 14:3014:30, 29 November 2018 diff hist +112 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 14 (a)/Hint 1 Created page with "The antiderivative of <math display="inline">(20-t)</math> is <math display="inline">\dfrac{(20-t)^2}{2}</math>."
- 14:2814:28, 29 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 13 (c) No edit summary
- 14:2714:27, 29 November 2018 diff hist −86 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 13 (c)/Hint 1 No edit summary current
- 14:2614:26, 29 November 2018 diff hist +1,298 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 13 (c)/Solution 1 Created page with "From <math display="block">g(c)=\dfrac{4c^3}{1+c^3}=4\dfrac{c^3+1-1}{1+c^3}=4-\dfrac{4}{1+c^3}=4-4(1+c^3)^{-1},</math> we differentiate using the power rule and chain rule to..."
- 14:1014:10, 29 November 2018 diff hist +142 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 13 (c)/Hint 1 Created page with "Notice that <math display="inline">g(c)</math> and the line <math display="inline">y(c)=rc</math> meet when <math display="inline">c=0</math>."
24 November 2018
- 22:2922:29, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 13 (a) No edit summary
- 22:2922:29, 24 November 2018 diff hist +375 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 13 (a)/Solution 1 Created page with "Following the Hint, the production rate is represented by the positive term, which is <math display="inline">\dfrac{4c^3}{1+c^3}</math>. Similarly, the consumption rate is rep..." current
- 22:1722:17, 24 November 2018 diff hist +80 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 13 (a)/Hint 1 Created page with "When the substance is produced, the rate of change is positive (and vice versa)." current
- 22:1622:16, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (d) No edit summary current
- 22:1622:16, 24 November 2018 diff hist +5 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (d)/Hint 1 No edit summary
- 22:1522:15, 24 November 2018 diff hist +790 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (d)/Hint 1 Created page with "Let the age be <math display="inline">T</math>. We need to solve the equation <math display="inline">A(-T)=1</math>: <math display="block">\dfrac45 e^{kT}=1</math> <math displ..."
- 22:0722:07, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (c) No edit summary
- 22:0622:06, 24 November 2018 diff hist +724 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (c)/Solution 1 Created page with "By the Hint, for <math display="inline">f(x)=\ln(x)</math>, <math display="inline">a=1</math>, we have <math display="inline">f'(x)=\dfrac1x</math>, <math display="inline">f(1..." current
- 22:0122:01, 24 November 2018 diff hist +163 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (c)/Hint 1 Created page with "Recall that the linear approximation of <math display="inline">y=f(x)</math> at <math display="inline">x=a</math> is <math display="inline">f(a)+f'(a)(x-a)</math>." current
- 21:5921:59, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (b) No edit summary
- 21:5921:59, 24 November 2018 diff hist +29 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (b)/Solution 1 No edit summary
- 21:5821:58, 24 November 2018 diff hist +949 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (b)/Solution 1 Created page with "Solving the differential equation in part (a), we have, as in the Hint, <math display="block">A(t)=A(0)e^{-kt}.</math> We are given that <math display="inline">A(0)=\dfrac45</..."
- 21:5321:53, 24 November 2018 diff hist +103 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (b)/Hint 1 Created page with "Recall that the solution of the differential equation is <math display="block">A(t)=A(0)e^{-kt}.</math>"
- 21:5121:51, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (a) No edit summary
- 21:5021:50, 24 November 2018 diff hist +303 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 12 (a)/Solution 1 Created page with "Let <math display="inline">A(t)</math> be the crater-free area. According to the description, <math display="block">A'(t)=-kA(t),</math> for some constant <math display="inlin..."
- 21:4821:48, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (b) No edit summary
- 21:4721:47, 24 November 2018 diff hist +50 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (b)/Hint 1 No edit summary current
- 21:4721:47, 24 November 2018 diff hist +455 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (b)/Solution 1 Created page with "We need to solve <math display="inline">f'(x)=0</math> near <math display="inline">x_0=1</math>. Using the Hint with <math display="inline">f'(x)</math> in place of <math disp..."
- 21:4421:44, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (b)/Hint 1 No edit summary
- 21:4321:43, 24 November 2018 diff hist +128 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (b)/Hint 1 Created page with "Recall that the formula for the first step in Newton’s Method is <math display="block">x_1=x_0-\dfrac{f(x_0)}{f'(x_0)}.</math>"
- 21:4121:41, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (a) No edit summary
- 21:4121:41, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (a)/Hint 1 No edit summary
- 21:4121:41, 24 November 2018 diff hist +540 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (a)/Solution 1 Created page with "Let us first compute the derivatives: <math display="block">f(x)=x^5-4x^2+2x,</math> <math display="block">f'(x)=5x^4-8x+2,</math> <math display="block">f''(x)=20x^3-8.</math>..."
- 21:3821:38, 24 November 2018 diff hist +149 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 11 (a)/Hint 1 Created page with "Recall the second derivative test: a critical point is a maximum (respectively minimum) if the second derivative is positive (respectively negative)."
- 21:3521:35, 24 November 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH102/December 2017/Question 10 (d) No edit summary
- 21:3421:34, 24 November 2018 diff hist +462 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 10 (d)/Solution 1 Created page with "By the Hint, for Patch 1 a secant line has maximum slope just a bit before <math display="inline">f_1</math> reaches its maximum. An approximate optimal time is <math display=..."
- 21:3121:31, 24 November 2018 diff hist +114 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 10 (d)/Hint 1 Created page with "By part (b), we need to find a secant line from the origin to the graph so that the slope is as large as possible." current
- 21:2921:29, 24 November 2018 diff hist +373 N Science:Math Exam Resources/Courses/MATH102/December 2017/Question 10 (c)/Solution 1 Created page with "In the graph for <math display="inline">f_1(t)</math> we see that the function reaches a maximum net energy gain. A possibility is that the the entire food patch has already b..." current