|
- algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b . . .
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 knowledge, and build their careers
- Evaluating $\\sqrt{119^2+120^2}$ with clever algebra
I'm wondering is it possible to start from $119^2+120^2$ and get $169^2$ algebraically without evaluating $119^2$ and $120^2$ directly? I could guess $169$ with approximation, $$\sqrt{119^2+120^2}\approx\sqrt{2\times 120^2}=120\sqrt2\approx120\times1 4$$ Which gives $168$ and checking the unit digits $169$ is a reasonable guess and it works!
- Evaluating $\\int R(X) \\sin(x) dx$ with residue theorem.
Evaluating a real definite integral using residue theorem 2 Evaluating a simple integral with the Cauchy
- 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
- sequences and series - Evaluating $\sum_{n=1}^{\infty} \frac{1}{n^2+1 . . .
While I know that $$\\sum_{n=1}^{\\infty} \\frac{1}{n^2} = \\frac{\\pi^{2}}{6}$$ But trying to evaluate this has left me stumped $$\\sum_{n=1}^{\\infty} \\frac{1}{n^2
- calculus - Evaluating $\int_0^ {\pi 2} \frac {\sqrt {\tan x}} {\sin x . . .
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 knowledge, and build their careers
- Evaluating $\\lim\\limits_{x\\to-3}\\frac{x^2-9}{2x^2+7x+3}$
$\begingroup$ The important thing to know at this level of evaluating limits is that if the numerator is zero, you can only conclude the whole thing is zero if the denominator is not zero We sometimes say $\frac00$ is indeterminate, because depending on how one gets to this symbolic expression $\frac00$, the actual limit may be any real number
- Evaluating $\\sum_{i=1}^{\\infty}\\frac{(i\\ln 2)^i}{2^ii!}$
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 knowledge, and build their careers
|
|
|