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- algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b . . .
Well, the image equation is a different equation? One has $\frac1 {2024}$ on the right, and the other has $2024$ on the right?
- integration - Evaluating $\iiint z (x^2+y^2+z^2)^ {−3 2}\,dx\,dy\,dz . . .
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 $\iiint_B (x^2+y^2+z^2)dV$ where $B$ is the ball of radius . . .
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 distance from
- Evaluating $ \lim\limits_ {n\to\infty} \sum_ {k=1}^ {n^2} \frac {n} {n . . .
How would you evaluate the following series? $$\\lim_{n\\to\\infty} \\sum_{k=1}^{n^2} \\frac{n}{n^2+k^2} $$ Thanks
- Evaluating $\\prod_{n=1}^{\\infty}\\left(1+\\frac{1}{2^n}\\right)$
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 $\int_0^1 \frac {\tan^ {-1} (x)\ln^2 (x)} {1+x}\,dx$
$$\color {green} {\int_0^1\frac {\ln^2 x\ln (1+x)} {1+x^2}\,dx= -2\Im \text {Li}_4 (i)+\frac {\pi^2}6G+\frac {\pi^3} {32}\ln2} $$ $$\color {red} {\int_0^1\frac {\tan
- Evaluating $\lim\limits_ {n\to\infty} e^ {-n} \sum\limits_ {k=0}^ {n . . .
I'm supposed to calculate: $$\\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
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