Tagged Questions

For basic questions about limits, derivatives, integrals, and applications, mainly of one-variable functions.

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Inner Product Examples, what is the points?

Example: For $-\pi<x<\pi$, $$x =-2 \sum_{n=1}^{\infty} \frac{(-1)^n}{n} \sin(nx)$$ and $$x^3 =-2 \sum_{n=1}^{\infty} \left( \frac{\pi^2}{n}-\frac{6}{n^3} \right)(-1)^n \sin(nx)$$ by ...
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Recommended Textbook for Integral Equation [on hold]

I am doing a self reading in preparation for the courses I have next semester of which Integral Equation is part of it. I keep on seeing very strange notations in the materials given to me by my ...
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Find $|\boldsymbol{a \times b}|$ (graph included) if $|\boldsymbol{a}| = 2$, $|\boldsymbol{b}| = 5$

I don't see how I have enough information to figure this one out. Here's what I'm thinking: \begin{align*} |\boldsymbol{a \times b}| & = |\boldsymbol{a}|~|\boldsymbol{b}|\sin(\theta)\\ ...
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As I can find the critical points of the function $\int_a^b (y^{2}+2(y')^{2}+(y'')^{2}) dx.$ [on hold]

Hi I'm stuck with a problem, greatly appreciate a suggestion to solve: As I can find the critical points of the function $$\int_a^b (y^{2}+2(y')^{2}+(y'')^{2}) dx.$$
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Evaluating a limit involving summation [duplicate]

Evaluate : $$\lim_{n\to\infty}\left(\dfrac{1}{e^{n}}\displaystyle \sum_{r=0}^{n} \dfrac{n^r}{r!}\right)$$ Numerical calculation suggests that the limit should be $\dfrac{1}{2}$. I tried ...
I am trying to understand the proof the Hilbert curve is nowhere differentiable. The Hilbert curve is defined as the mapping $f_h: I \to \mathcal{Q}$ where I in the unit interval in $\mathbb{R}$ and ...
In the following example i am looking to find the volume of the solid bounded above by the plane $z = y$ and below by the paraboloid $z = x^2 +y^2$ by the method of cylindridical coordinates. ...