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Hello Lovely people of the Overflow :) I am working on a homework assigntment for my linear algebra class and i am stumped on this pesky question which is...
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Proof from Apostol: (Annotations mine) If $f$ has a continuous derivative $f'$ on the interval $[y, x]$, where $0 < y < x$, then $$\sum\limits_...
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A quiz is 1 hour long, and has two questions. The time you give to Q1 is represented by the random variable $X$ which has the following pdf: $$f_X(x)=12x(...
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If $(f_n)$ is a pointwise convergent, uniformly bounded sequence of measurable functions on and interval $I:[0,1]$, then: $$\begin{align*} \lim_{n\to\inft...
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SO the question is, is $f(x)=1/x$ an injective, surjective, bijective or none of the above function? The domain is all real numbers except 0 and the range...
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I was trying to solve for the moment of inertia of a solid and a hollow cylinder, and I faced a small problem. I looked through online resources and found...
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The definition of the integral below is what I usually call the "High School definition," because that's usually where I've seen it in use. Take...
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I know how to find the distance between a point and a line, not between two lines. Find the shortest distance between the lines $(-1,1,4) + t(1,1,-1)$ and...
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So I have the equation $\frac{d}{dx}[\cos(2x)-3\sin(x)-1]$ What I did was simplify $\cos(2x)$ to $1-2\sin^2(x)$ by applying the double angle formula. Here...
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