Question

Is $\lim_{n\to \infty}\int_0^{\pi/2} \frac{x^{\frac 1n}+\sin x}{\tan x+x^{\frac 1n}} dx=\int_0^{\pi/2} \frac{1+\sin x}{\tan x+1} dx=1.62..$?

score 97 · Answer 1 · 2018-04-13 14:07:18

97

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Is $\lim_{n\to \infty}\int_0^{\pi/2} \frac{x^{\frac 1n}+\sin x}{\tan x+x^{\frac 1n}} dx=\int_0^{\pi/2} \frac{1+\sin x}{\tan x+1} dx=1.62..$?

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List Question

Is $\lim_{n\to \infty}\int_0^{\pi/2} \frac{x^{\frac 1n}+\sin x}{\tan x+x^{\frac 1n}} dx=\int_0^{\pi/2} \frac{1+\sin x}{\tan x+1} dx=1.62..$?

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A question on bounded sequences of real numbers.

Uniform Convergence of Sequence of Bounded Operators

If $X$ can be described by sequences, then it is metrizable

How to prove $\lim _{n \to \infty} S_n=\infty$ for partial sums of a divergent series?

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