mathstudent

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I am currently a 1st year Advanced Mathematics University Student. I very much appreciate all the kind people in the stack exchange community and thank you all in advance for sharing your knowledge and expertise with me.

	480 reputation	bio	website		visits	member for	1 year, 2 months
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39 Questions

views newest activity votes

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514

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Show that $f'$ is not continuous at 0 for the following function:

jun 13 '12 at 21:19 user17762 76.2k

votes

answer

140

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Find $ \int x^{-n}(1-x)^{-1}\,dx. $

calculus integration

oct 3 at 2:09 Gerry Myerson 85.9k

votes

answer

113

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Using the chain rule to compute $f_\theta$ given $f_x$ and $f_y$

homework multivariable-calculus

jun 19 '12 at 18:50 Community♦ 1

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answer

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Evaluating $\lim_{y \to 0^+} (\cosh (3/y))^y$

homework trigonometry limit

jun 11 '12 at 8:49 Gigili 3,153

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kviews

What is $\lim_{(x,y)\to(0,0)} (x^3+y^3)/(x^2-y^2)$?

calculus limit

jun 4 '12 at 18:22 JLA 847

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answer

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Suppose that $ x(t)$ satisfies the differential equation $ x' + x^3 = 2x $ Find the differential equation for $ v = \frac{1}{x^2}$

differential-equations

oct 11 at 2:51 Peter Tamaroff 25.6k

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108

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Does the series $ \sum_{n=0}^{\infty}\frac{n^4}{4^n} $ converge? Use a suitable test to justify.

calculus sequences-and-series

sep 27 at 5:23 kjetil b halvorsen 884

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193

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Calculate the integral $xF(x) \, dx$, between $0$ and $1$

homework calculus

sep 25 at 4:36 Michael Hardy 48.1k

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109

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What is the 35th derivative of $f(x) = e^{x^{10}} $at $x = 0$?

homework calculus taylor-expansion

jun 2 '12 at 2:16 Peter Tamaroff 25.6k

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227

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For the epsilon-delta definition of limits, can you always pick $\delta$ to be $\epsilon/4$?

calculus limit

jun 1 '12 at 11:42 rschwieb 20.9k

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372

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Factorize the polynomial $P(z) = z^4 - 2z^3-z^2+2z+10$, into linear and/or quadratic factors with real coefficients

homework calculus complex-numbers

jun 1 '12 at 7:26 Baby Dragon 833

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answer

111

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what is $\lim\limits_{x\to\infty}\cosh x/x!$?

homework calculus

may 28 '12 at 3:01 Arturo Magidin 158k

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130

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What is the Taylor series for $g(x) =\frac{ \sinh(-x^{1/2})}{(-x^{1/2})}$, for $x < 0$?

homework calculus taylor-expansion

jun 11 '12 at 9:04 Gigili 3,153

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110

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sketch set satisfying $|z-2|+|z+2|\le5$

homework complex-numbers

jun 1 '12 at 3:21 Vasea Igor 19

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For $\alpha > 0$, define the function: $g(x) = |x|^\alpha \cos(1/x^2)$, for $x \neq 0$, $g(x) = 0$, when $x = 0$

homework calculus limit

may 31 '12 at 0:53 anon 39.9k

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What is $\lim\limits_{k \to 0}{f(k) = 2 + k^{\frac{3}{2}}\cos {\frac{1}{k^2}}}$

homework calculus limit

apr 25 '12 at 16:11 J. M. 38.9k

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answer

153

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$ax+by+cz=d$ is the equation of a plane in space. Show that $d'$ is the distance from the plane to the origin.

linear-algebra

may 8 at 9:43 mathstudent 480

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119

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Let a, b, c be three nonzero vectors, any two of which are perpendicular. Prove that these 3 vectors are linearly independent.

linear-algebra

may 8 at 9:41 mathstudent 480

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190

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Improper integral $\int^{\frac{\pi}{2}}_0 (\operatorname{csc} x - \frac{1}{x})\, dx$

homework calculus integral improper-integrals

sep 26 at 8:49 martini 15.8k

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answer

319

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For this non-linear differential equation: $ xy' = y + ax \sqrt{x^2+y^2} $, where $ x>0 $ and $ a>0$ is a constant

homework differential-equations

sep 26 at 7:08 Avatar 8,345

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answer

299

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Find the 2nd order Taylor Polynomial of y(x) about x = 0, given:

homework algebra-precalculus differential-equations integration

sep 23 at 5:28 Rod Carvalho 1,697

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196

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Use the identity $\cos(A-B) -\cos(A+B) = 2\sin(A)\sin(B)$ to prove another identity and evaluate a sum

homework sequences-and-series trigonometry

aug 10 at 16:13 Américo Tavares 20.7k

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answer

102

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$\lim _{(x,y)\rightarrow (0,0)} \ln(\sin(x^2+y^2))=?$

homework calculus limit

jun 6 '12 at 1:52 rschwieb 20.9k

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Find the largest value of $d$ of the form $d = A\varepsilon^b$ such that the following statement is correct:

homework calculus limit

jun 5 '12 at 4:14 mathstudent 480

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Use the Taylor Polynomial of order $3$ for $f(x)=\sin x$ about $x=0$ and its remainder term to prove that: $x-(x^3/6)<\sin x$, for $0<x<\pi$

homework calculus

jun 4 '12 at 3:20 Michael Boratko 2,924

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128

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How to use the Mean Value Theorem to prove the following statement:

homework calculus limit proof-strategy

jun 2 '12 at 11:15 Norbert 20.2k

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279

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Evaluating $\lim\limits_{x\to\infty} \frac{\ln(x^2+4)}{\sinh^{-1}x}$

homework limit

jun 2 '12 at 1:49 mathstudent 480

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202

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Prove the substitution law for limits (using the $\epsilon$-$\delta$ definition)

homework calculus limit

apr 12 '12 at 1:40 mathstudent 480

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488

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Use the Intermediate Value Theorem to prove $f:[0,1]\to [0,1]$ continuous and $C\in[0,1]$, there is some $c \in [0,1]$ such that $f(c) = C$.

real-analysis analysis

apr 10 '12 at 22:32 Beni Bogosel 10.5k

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191

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Show that for any complex number W, there exists a non-zero complex number Z such that Z + 1/Z = W

complex-analysis polynomials

mar 20 '12 at 18:55 Michael Hardy 48.1k