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calculus - Evaluating integrals with sigma notation - Mathematics …
I am suppose to use Theorem 4 in my books (just the limit as n approaches infinity of a summation representing the function). I am trying to evaluate $$ \\int_2^5 (4-2x) dx$$ I really …
Is there a way to get trig functions without a calculator?
In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a …
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 $ \\lim\\limits_{n\\to\\infty} \\sum_{k=1}^{n^2} \\frac{n}{n ...
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 ...
Easy way to compute logarithms without a calculator?
Feb 14, 2016 · I would need to be able to compute logarithms without using a calculator, just on paper. The result should be a fraction so it is the most accurate. For example I have seen this …
linear algebra - Show that $\det(A) = 0$ without directly evaluating ...
Oct 20, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
How to deal with negative area when evaluating a definite integral
Jan 17, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
integration - Help evaluating triple integral over tetrahedron ...
I agree entirely with the accepted answers; that is how the integral should be attempted analytically. However, if you wish to compute integrals of this form over the unit tetrahedron …
How to prove that limit of arctan(x) as x tends to infinity, is $\\pi/2$?
While working on some probability question, I had to evaluate $\lim_{x \to \infty} \arctan(x)$. I knew the answer intuitively as $\pi/2$, yet I cannot figure out how to prove it by elementary …
calculus - evaluating a double integral over a region
Mar 5, 2014 · In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows: Sketch the region D and express the double integral as an iterated …
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