User contributions for DanielSheinbaumFrank
2 February 2018
- 23:0423:04, 2 February 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 09 No edit summary
- 23:0323:03, 2 February 2018 diff hist +150 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 09/Hint 1 Created page with "Rewrite <math> 6x^3 e^{-x^2}</math> as a product so that one of the factors is the derivative of <math>e^ {-x^2}</math> and use integration by parts."
- 23:0123:01, 2 February 2018 diff hist +765 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 09/Solution 1 Created page with "Let us rewrite the integrand, so that <math>\int_{0}^{\infty} 6x ^3 e^{-x^2} dx = -3\int_{0}^{\infty}x^ 2 (-2x e^{-x^2}) dx</math> Use integration by parts where <math> f^{..."
- 22:3722:37, 2 February 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 08 No edit summary
- 22:3622:36, 2 February 2018 diff hist +178 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 08/Hint 1 Created page with "Factorize the denominator into monimials. Use partial fraction decomposition to split the integrand into simpler expressions with denominator one of factors (up to multiplicity)." current
- 22:3322:33, 2 February 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 08/Solution 1 No edit summary
- 22:3122:31, 2 February 2018 diff hist +986 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 08/Solution 1 Created page with "First note that the denominator of the integrand factorizes as : <math> \frac{x-8}{x^ 3 - 4x^ 2 + 4x} = \frac{x-8}{x} \frac{1}{(x-2)^ 2} = \frac{1}{(x-2)^ 2} - \frac{8}{x(x-2..."
30 January 2018
- 01:3901:39, 30 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 05 (a) No edit summary
- 01:3801:38, 30 January 2018 diff hist +317 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 05 (a)/Hint 1 Created page with "Use integration by parts, using <math> f^ {\prime}(x) = \sin x </math>. Use the trig identity <math> \cos ^ 2 x = 1-sin^ 2 x</math> to have an expression with only powers of..."
- 01:3501:35, 30 January 2018 diff hist +1,248 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 05 (a)/Solution 1 Created page with "Using integration by parts <math> \int f^ {\prime}g = fg - \int fg^ {\prime}</math>, we pick <math> f^{\prime}(x) = \sin x ,\, g(x) = \sin^ {4}(x)</math>, which yields <math..."
- 00:3200:32, 30 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (b) No edit summary
- 00:3100:31, 30 January 2018 diff hist +297 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (b)/Hint 1 Created page with "The difference between the integral and the midpoint rule of order 6 will at most be the error, given by the formula above. To bound the 2nd derivative of <math>f(x) = x\sin x..."
- 00:2500:25, 30 January 2018 diff hist +1,018 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (b)/Solution 1 Created page with "Using the information given above all we need to find is <math>K</math> and replace the values of <math>a = 0,\, b= \pi,\, n = 6</math> in the formula for the error <math>\fra..."
- 00:0000:00, 30 January 2018 diff hist +12 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (a)/Solution 1 No edit summary
29 January 2018
- 23:5423:54, 29 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (a) No edit summary
- 23:5423:54, 29 January 2018 diff hist +247 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (a)/Hint 1 Created page with "Use the formulas for the centroid <math> \bar{x} = \frac{1}{A}\int_{a}^{b} x(f(x) - g(x))dx</math> <math> \bar{y} = \frac{1}{A} \int_{a}^{b} \frac{f(x)+g(x))}{2}(f(x) - g(x)..." current
- 23:5123:51, 29 January 2018 diff hist +729 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (a)/Solution 1 Created page with "The points of intersection are given by <math> 3 = 3x^4 </math>, which implies <math>x = -1,1</math> Using the formulas for the centroid: <math> \bar{x} = \frac{1}{A}\int_{a}..."
- 23:1123:11, 29 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 03 (a) No edit summary
- 23:1123:11, 29 January 2018 diff hist +97 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 03 (a)/Hint 1 Created page with "Find the points of intersection of the 2 graphs to determine the integration limits for the area."
- 23:0923:09, 29 January 2018 diff hist +507 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 03 (a)/Solution 1 Created page with "First find the points of intersection, thus: <math> y = x-8 = -x^2 +7x - 16 </math>, hence <math> -x^2 +6x -8 = 0</math>. Using the quadratic formula we have: <math>x = \fr..."
27 January 2018
- 21:1621:16, 27 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 02 (b) No edit summary
- 21:1521:15, 27 January 2018 diff hist +101 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 02 (b)/Hint 1 Created page with "Use the identity <math>\sec^ {2} u = \tan ^{2} u +1</math> to simplify the inside of the square root." current
- 21:1321:13, 27 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 02 (b)/Solution 1 No edit summary
- 21:1121:11, 27 January 2018 diff hist +616 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 02 (b)/Solution 1 Created page with "We want an expression that simplifies the one on the square root. Note that <math> x^ 2+2x+10 = (x+1)^ 2 + 3^2</math>, thus one of the expressions with a -1 on it will help u..."
- 20:3620:36, 27 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 02 (a) No edit summary
- 20:3420:34, 27 January 2018 diff hist +153 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 02 (a)/Hint 1 Created page with "Isolate <math>y</math> in both the expressions given on the question. To the right means it appears with a positive sign and to left with a negative one."
- 20:3020:30, 27 January 2018 diff hist +436 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 02 (a)/Solution 1 Created page with "From the first equation we obtain <math> y = \sqrt{1-x} </math> and from the 2nd one we obtain <math> y = \sqrt{\frac{5-x}{2}} </math>. We see that the only options with these..."
- 20:1920:19, 27 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (d) No edit summary
- 20:1820:18, 27 January 2018 diff hist +116 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (d)/Hint 1 Created page with "Use chain rule to integrate on one side with respect to <math>y</math> and the other with respect to <math>x</math>." current
- 20:1520:15, 27 January 2018 diff hist +483 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (d)/Solution 1 Created page with "Using chain rule we have <math>\frac{dy}{dx} = \frac{\cos x}{2y}</math>, hence <math>\int y{dy} = \int \frac{\cos x dx}{2}</math> and thus <math>\frac{y^ 2}{2} = \frac{\sin x}..."
- 19:4619:46, 27 January 2018 diff hist +40 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (b)/Hint 2 Created page with "Use the fundamental theorem of calculus."
- 19:4619:46, 27 January 2018 diff hist +57 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (b)/Hint 1 Created page with "Think about the derivative of <math>\sqrt{x^ 2-3}</math>."
- 19:4519:45, 27 January 2018 diff hist +225 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (b)/Solution 1 Created page with "We can use the fundamental theorem of calculus so that <math> \int \frac{3x}{\sqrt{x^ 2-3}} = 3\int \frac{x}{\sqrt{x^ 2-3}} = 3\int(\sqrt{x^ 2-3})^{\prime} = 3\sqrt{x^ 2-3}</..."
- 19:3319:33, 27 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (a) No edit summary
- 19:3119:31, 27 January 2018 diff hist +2 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (a)/Solution 1 No edit summary
- 19:3019:30, 27 January 2018 diff hist +2 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (a)/Solution 1 No edit summary
- 19:2919:29, 27 January 2018 diff hist +13 Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (a)/Solution 1 No edit summary
- 19:2719:27, 27 January 2018 diff hist +103 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (a)/Hint 1 Created page with "For negative values of <math>x,\, 1-|x| = 1+x</math> and for positive values <math>1-|x| = 1-x</math>." current
- 19:2719:27, 27 January 2018 diff hist +570 N Science:Math Exam Resources/Courses/MATH101/April 2017/Question 01 (a)/Solution 1 Created page with "For negative values of <math>x,\, 1-|x| = 1+x</math> and for positive values <math>1-|x| = 1-x</math>. We can split the integral so that one part has only the negative values..."
26 January 2018
- 22:1122:11, 26 January 2018 diff hist +1 Science:Math Exam Resources/Courses/MATH102/December 2015/Question 07 No edit summary current
- 22:0922:09, 26 January 2018 diff hist +2 Science:Math Exam Resources/Courses/MATH102/December 2015/Question 19 (e) No edit summary current
- 22:0922:09, 26 January 2018 diff hist +10 Science:Math Exam Resources/Courses/MATH102/December 2015/Question 19 (e)/Solution 1 No edit summary current
- 22:0522:05, 26 January 2018 diff hist +2 Science:Math Exam Resources/Courses/MATH102/December 2015/Question 19 (d) No edit summary current
- 22:0122:01, 26 January 2018 diff hist +2 Science:Math Exam Resources/Courses/MATH102/December 2015/Question 19 (c) No edit summary current
- 21:5821:58, 26 January 2018 diff hist +1 Science:Math Exam Resources/Courses/MATH102/December 2015/Question 11 No edit summary current
25 January 2018
- 22:4722:47, 25 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 04 (c) No edit summary
- 22:4722:47, 25 January 2018 diff hist +249 N Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 04 (c)/Hint 1 Created page with "The solution to the system of linear differential equations is <math> \begin{bmatrix} R(t) \\ J(t)\\ \end{bmatrix} = e^{At}\begin{bmatrix} R_0 \\ J_0\\ \end{bmatrix}</math>. R..."
- 22:4422:44, 25 January 2018 diff hist +849 N Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 04 (c)/Solution 1 Created page with "Since we know the eigenvalues and eigenvectors, using the equation <math> \begin{bmatrix} R(t) \\ J(t)\\ \end{bmatrix} = e^{At}\begin{bmatrix} R_0 \\ J_0\\ \end{bmatrix}</mat..."
- 22:1322:13, 25 January 2018 diff hist 0 Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 04 (b) No edit summary
- 22:1022:10, 25 January 2018 diff hist +643 N Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 04 (b)/Solution 1 Created page with "The eigenvector equation is: <math> \begin{bmatrix} 1 & 4 \\ -2 & -3\\ \end{bmatrix}\begin{bmatrix} R \\ J \\ \end{bmatrix} = (-1\pm 2i)\begin{bmatrix} R \\ J \\ \end{bmatr..."