I am trying to evaluate the integral $$\int \frac{1}{1+x^4} \mathrm dx.$$ The integrand $\frac{1}{1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the …

Evaluating integrals with sigma notation. Ask Question Asked 13 years, 2 months ago. Modified 8 years, 1 ...

I'm supposed to calculate: $$\\lim_{n\\to\\infty} e^{-n} \\sum_{k=0}^{n} \\frac{n^k}{k!}$$ By using WolframAlpha, I might guess that the limit is $\\frac{1}{2 ...

Here's another approach. First, note that $$\begin{eqnarray*} \sum_{k=n^2+1}^\infty \frac{n}{n^2+k^2} &<& \sum_{k=n^2+1}^\infty \frac{n}{k^2} \\ &\le& n\int_{n^2 ...

Aug 25, 2015 · The Dirac Delta function $\delta(x)$ is very cool in the sense that $$ \delta(x) = \begin{cases} +\infty, \, & x =0 \\ 0, \, & x \ne 0 \end{cases} $$

Apr 24, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …

Feb 6, 2019 · $\begingroup$ @leonbloy Yes, I do know that even if the limit has the same value along every LINE that passes through the point we are evaluating the limit at, limit may not …

May 22, 2014 · So if you are evaluating a trigonometric function at a number without this symbol, then I would assume that it is in radians. Even though you can use both, often people will insist …

I need to learn how to find the definite integral of the square root of a polynomial such as: $$\\sqrt{36x + 1}$$ or $$\\sqrt{2x^2 + 3x + 7} $$ EDIT: It's not guaranteed to be of the same …