User contributions for GaloHigueraRojo
20 February 2013
- 23:4223:42, 20 February 2013 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2012/Question 05 No edit summary
- 23:4223:42, 20 February 2013 diff hist +1,173 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 05/Solution 1 Created page with "We will use the ratio test: <math> \begin{align} \lim_{n\to \infty} \left|\frac{a_{n+1}}{a_n}\right|&=\lim_{n\to \infty}\left| \frac{\frac{(x-1)^{n+1}}{2^{n+1}(n+3)}}{\frac{(..."
- 23:0723:07, 20 February 2013 diff hist +80 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 05/Hint 1 Created page with "Use the ratio test to figure out for which values of x does the series converge."
- 23:0023:00, 20 February 2013 diff hist +629 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (c)/Solution 1 Created page with "We will use the integral test. Note that <math> \int_2^\infty \frac{dx}{xln(x)^{101}}=\lim_{a\to \infty} \int_2^a \frac{dx}{xln(x)^{101}} </math> We can calculate <math> \i..."
- 22:4622:46, 20 February 2013 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (c)/Statement No edit summary
- 22:4522:45, 20 February 2013 diff hist +1 Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (c)/Hint 1 No edit summary
- 22:4522:45, 20 February 2013 diff hist +55 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (c)/Hint 1 Created page with "Can you integrate <math> \frac{1}{x(lnx)^{101} </math>?"
- 22:4222:42, 20 February 2013 diff hist +692 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (b)/Solution 1 Created page with "We want to use the Ratio test, so we look at the limit: <math> \begin{align} \lim_{n\to \infty} \big|\frac{a_n}{a_{n+1}}\big|&=\lim_{n\to \infty} \frac{\frac{(2n+2)!}{((n+1..."
- 22:2022:20, 20 February 2013 diff hist +61 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (b)/Hint 2 Created page with "Remember that <math> n!=n\cdot (n-1) \cdots 2\cdot 1. </math>"
- 22:1822:18, 20 February 2013 diff hist +41 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (b)/Hint 1 Created page with "Do you remember what the Ratio test says?"
- 22:1722:17, 20 February 2013 diff hist +456 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (a)/Solution 1 Created page with "We will compare our series with <math> \displaystyle \sum_{n=0}^\infty \frac{1}{n^4} .</math> So we look at the limit: <math> \lim_{n\to \infty} \frac{(\frac{n^2-sin(n)}{n^6+..."
- 22:0822:08, 20 February 2013 diff hist +27 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (a)/Hint 3 Created page with "How about <math> k=4</math>"
- 22:0822:08, 20 February 2013 diff hist +101 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (a)/Hint 2 Created page with "Use a comparison test with a series like <math>\displaystyle \sum_{n=0}^\infty \frac{1}{n^k} </math>."
- 22:0422:04, 20 February 2013 diff hist +128 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 04 (a)/Hint 1 Created page with "Use the fact that sums of the form <math>\displaystyle \sum_{n=0}^\infty \frac{1}{n^k} </math> converge for <math>k\geq 2</math>"
- 22:0022:00, 20 February 2013 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (c) No edit summary
- 22:0022:00, 20 February 2013 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (d) No edit summary
- 21:5921:59, 20 February 2013 diff hist +343 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (d)/Solution 1 Created page with "The integral is equal to the sum of the two integrals <math>\int_{-\infty}^0\frac{x}{x^2+1}dx+\int_0^\infty\frac{x}{x^2+1}dx </math>. Note that <math>\int_0^\infty\frac{x}{x^2..."
- 21:5321:53, 20 February 2013 diff hist +55 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (d)/Hint 1 Created page with "Split this as two improper integrals. Do they converge?"
- 21:5221:52, 20 February 2013 diff hist +623 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (c)/Solution 1 Created page with "We want to write the integrand using partial fractions: <math>\frac{4x+8}{(x-2)(x^2+4)}=\frac{A}{x-2}+\frac{Bx+C}{x^2+4}=\frac{A(x^2+4)+(Bx+C)(x-2)}{(x-2)(x^2+4)} </math> Co..."
- 21:3621:36, 20 February 2013 diff hist +21 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (c)/Hint 1 Created page with "Use partial fractions"
- 21:3621:36, 20 February 2013 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (b) No edit summary
- 21:3521:35, 20 February 2013 diff hist +639 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (b)/Solution 1 Created page with "We can write the integral as <math> \int_0^3(x+1)\sqrt{9-x^2}dx=\int_0^3x\sqrt{9-x^2}dx+\int_0^3\sqrt{9-x^2}dx</math>. Now we compute: for <math>\int_0^3x\sqrt{9-x^2}dx </ma..."
- 21:2421:24, 20 February 2013 diff hist +83 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (b)/Hint 2 Created page with "The integral <math> \int_0^3 \sqrt{9-x^2} </math> can be interpreted geometrically."
- 21:2121:21, 20 February 2013 diff hist +75 N Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (b)/Hint 1 Created page with "Try to write the integral as a sum of two integrals that you can calculate."
26 March 2012
- 00:1900:19, 26 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH220/April 2005/Question 06 No edit summary
- 00:1900:19, 26 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH220/April 2005/Question 06/Solution 1 No edit summary
- 00:1800:18, 26 March 2012 diff hist +628 Science:Math Exam Resources/Courses/MATH220/April 2005/Question 06/Solution 1 No edit summary
- 00:1100:11, 26 March 2012 diff hist +66 N Science:Math Exam Resources/Courses/MATH220/April 2005/Question 06/Hint 1 Created page with "Show that you can get every positive integer except 1, 2, 4 and 7." current
25 March 2012
- 06:5806:58, 25 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH220/April 2005/Question 10 No edit summary
- 06:5706:57, 25 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH220/April 2005/Question 10/Hint 1 No edit summary
- 06:5706:57, 25 March 2012 diff hist +577 N Science:Math Exam Resources/Courses/MATH220/April 2005/Question 10/Solution 1 Created page with "Since <math> f </math> is bounded there exists <math> M\in \mathbb{R} </math> such that <math> |f(n)|<M </math> for all <math> n\in \mathbb{N} </math>. We will show that <mat..."
- 06:3006:30, 25 March 2012 diff hist +184 N Science:Math Exam Resources/Courses/MATH220/April 2005/Question 10/Hint 1 Created page with "Shaw that if <math> \{a_n\} </math> is a sequence converging to zero and <math> M\in \mathbb{R} </math> is a constant then the sequence <math> \{Ma_n\} </math> also converges..."
- 05:4705:47, 25 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH220/April 2005/Question 05 No edit summary
- 05:4605:46, 25 March 2012 diff hist +614 N Science:Math Exam Resources/Courses/MATH220/April 2005/Question 05/Solution 1 Created page with "We use induction. In the base case when <math> n=1 </math> we have <math> |a_1|\leq |a_1| </math> so the statement is true. Induction step: we assume <math> |\sum_{i-1}^na_i..."
- 05:3705:37, 25 March 2012 diff hist +63 N Science:Math Exam Resources/Courses/MATH220/April 2005/Question 05/Hint 1 Created page with "Use that <math> \sum_{i=1}^na_i=\sum_{i=1}^{n-1}a_i+a_n </math>"
24 March 2012
- 07:0907:09, 24 March 2012 diff hist +1 Science:Math Exam Resources/Courses/MATH220/April 2005/Question 11 No edit summary
- 07:0807:08, 24 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH220/April 2005/Question 11 No edit summary
- 07:0707:07, 24 March 2012 diff hist +1,597 N Science:Math Exam Resources/Courses/MATH220/April 2005/Question 11/Solution 1 Created page with "Note that if <math>x^2<5 </math> then <math> |x|<\sqrt{5} </math>. In other words <math> x\in (-\sqrt{5},\sqrt{5}) </math> for all <math> x\in M </math>. In particular <math> ..."
23 March 2012
- 23:5623:56, 23 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2010/Question 03 (a) No edit summary
- 23:5523:55, 23 March 2012 diff hist +684 N Science:Math Exam Resources/Courses/MATH101/April 2010/Question 03 (a)/Solution 1 Created page with "We look for an expression in partial fractions of the form: <math> \frac{x^2-9}{x(x^2+9)}=\frac{A}{x}+\frac{Bx+C}{x^2+9} </math> Which translates to: <math> x^2-9=Ax^2+9A+B..."
- 23:3823:38, 23 March 2012 diff hist +21 N Science:Math Exam Resources/Courses/MATH101/April 2010/Question 03 (a)/Hint 1 Created page with "Use partial fractions"
- 07:0407:04, 23 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2010/Question 08 No edit summary
- 07:0207:02, 23 March 2012 diff hist +759 N Science:Math Exam Resources/Courses/MATH101/April 2010/Question 08/Solution 1 Created page with "The interval has size 1 so <math> \Delta x=\frac{1}{n} </math>. The interval is <math> [0,1] </math> so <math> x_i=\frac{i}{n} </math>. In this case <math> f(x)=6-3x^2 </math>..."
- 06:4206:42, 23 March 2012 diff hist +1 Science:Math Exam Resources/Courses/MATH101/April 2010/Question 08/Hint 1 No edit summary
- 06:4206:42, 23 March 2012 diff hist +65 Science:Math Exam Resources/Courses/MATH101/April 2010/Question 08/Hint 1 No edit summary
- 06:3706:37, 23 March 2012 diff hist +43 N Science:Math Exam Resources/Courses/MATH101/April 2010/Question 08/Hint 1 Created page with "Split the integral and factor the constants"
- 06:3306:33, 23 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2010/Question 09 No edit summary
- 06:3206:32, 23 March 2012 diff hist +1,104 N Science:Math Exam Resources/Courses/MATH101/April 2010/Question 09/Solution 1 Created page with "First we solve the integral considering <math> x </math> as a constant: <math> \begin{align} g(x)&=\int_0^1(xe^t-t)^2dt\\ &=\int_0^1(x^2e^{2t}-2xe^tt+t^2)dt\\ &=x^2\int_0^1e^..."
- 06:0106:01, 23 March 2012 diff hist +66 N Science:Math Exam Resources/Courses/MATH101/April 2010/Question 09/Hint 1 Created page with "We can consider <math> x </math> as a constant inside the integral"
3 March 2012
- 01:4401:44, 3 March 2012 diff hist 0 Science:Math Exam Resources/Courses/MATH101/April 2010/Question 01 (f) No edit summary