integration - Evaluating $\sum_ {m=0}^\infty \sum_ {n=0}^\infty …
Nov 11, 2025 · I am evaluating the following integral: $$\\int_0^{1} \\left(\\tanh^{-1}(x) + \\tan^{-1}(x)\\right)^2 \\; dx$$ After using the Taylor series of the two functions, we ...
algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b ...
Feb 21, 2025 · Well, the image equation is a different equation? One has $\frac1 {2024}$ on the right, and the other has $2024$ on the right?
calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
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 integral if I ...
Evaluating $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1/2x}}{x} $ without ...
Sep 11, 2024 · The following is a question from the Joint Entrance Examination (Main) from the 09 April 2024 evening shift: $$ \lim_ {x \to 0} \frac {e - (1 + 2x)^ {1/2x}} {x} $$ is equal to: (A) …
integration - Evaluating $\iiint z (x^2+y^2+z^2)
Jul 29, 2020 · Spherical Coordinate Homework Question Evaluate the triple integral of $f (x,y,z)=z (x^2+y^2+z^2)^ {−3/2}$ over the part of the ball $x^2+y^2+z^2\le 81$ defined by ...
Evaluating $\lim\limits_ {n\to\infty} e^ {-n} \sum\limits_ {k=0}^ {n ...
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 ...
Evaluating $\\prod_{n=1}^{\\infty}\\left(1+\\frac{1}{2^n}\\right)$
Sep 13, 2016 · Compute:$$\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$$ I and my friend came across this product. Is the product till infinity equal to $1$? If no, what is the answer?
Evaluating $\cos (i)$ - Mathematics Stack Exchange
Nov 27, 2020 · This is too long for a comment. So I will write it as an answer. Lets assume the definition of $\exp$ function via power series. Then it is well defined on the complex plane as …
Evaluating $\int_ {0}^1\int_ {0}^1 xy\sqrt {x^2+y^2}\,dy\,dx$
Calculate the iterated integral: $$\int_ {0}^1\int_ {0}^1 xy\sqrt {x^2+y^2}\,dy\,dx$$ I'm stumped with this problem. Should I do integration by parts with both variables or is there another way to do ...
Evaluating $\iiint_B (x^2+y^2+z^2)dV$ where $B$ is the ball of …
The question asks to use spherical coords. My answer is coming out wrong and symbolab is saying I'm evaluating the integrals correctly so my set up must be wrong. Since $\\rho$ is the …