calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
The integrand 1 1+x4 1 1 + x 4 is a rational function (quotient of two polynomials), so I could solve the integral if I can find the partial fraction of 1 1+x4 1 1 + x 4. But I failed to factorize 1 +x4 1 + …
Evaluating integrals with sigma notation - Mathematics Stack …
Evaluating integrals with sigma notation Ask Question Asked 13 years, 3 months ago Modified 8 years, 2 months ago
Problem evaluating limits with the variable in the exponent
I have problem evaluating limits with the variable in power, like the following limits: limx→0(1 + sin 2x)1 x lim x → 0 (1 + sin 2 x) 1 x limx→∞(2x+5 2x−1)2x lim x → ∞ (2 x + 5 2 x 1) 2 x I asked …
Evaluating $\\sqrt{1 + \\sqrt{2 + \\sqrt{4 + \\sqrt{8 + \\ldots}}}}$
Inspired by Ramanujan's problem and solution of 1 + 2 1 + 3 1 +, I decided to attempt evaluating the infinite radical
complex numbers - Evaluating $2^i$ - Mathematics Stack Exchange
Oct 17, 2017 · It is obvious that we should use Euler's formula, but the fact that $\\Vert e^{i \\alpha} \\Vert = 1$ (while the base is 2) brings difficulty of using it. Can anyone think of a way …
Evaluating a Complex Integral involving Bessel Function
Jan 12, 2025 · Evaluating a Complex Integral involving Bessel Function Ask Question Asked 6 months ago Modified 6 months ago
Evaluating $\\lim\\limits_{x\\to-3}\\frac{x^2-9}{2x^2+7x+3}$
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 0 …
integration - Evaluating $\Gamma$-function at $x=1/2
May 28, 2021 · I was following an explanation of the gamma function and everything made sense until the author evaluated the function at 1/2. The $\Gamma$-function is defined as the …
Evaluating $\\lim\\limits_{n\\to\\infty} e^{-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 ...
calculus - Evaluating $\int_0^\pi \log (\sin x) \mathrm dx$ using ...
Evaluating ∫π 0 log(sin x)dx ∫ 0 π log (sin x) d x using Riemann sums Ask Question Asked 13 years, 3 months ago Modified 4 months ago