Nanayajitzuki

 5 If $(f\circ g)(x)=\tan^2x$ and $g(x)=\sqrt{\cos2x}$ then find $f(x)=?$ 4 How find the limit of $\lim\limits_{n\to \infty }\left(n-1\right)!$ 3 Prove $\lim_{n\to \infty}\int_0^Tg(x)h(nx) dx=\cfrac{1}{T}(\int_0^Tg(x)dx)(\int_0^Th(x)dx)$ 2 Integrals depending on a parameter: $\int_{0}^{\pi/2} \ln(a^2\sin^2{x} + \cos^2{x})dx$ 2 What value does $\sum_{n=1}^{\infty} \dfrac{1}{4n^2+16n+7}$ converge to?

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### Questions (4)

 4 Evaluate $\sum_{n=1}^{\infty} {\frac1{n} (H_{2n}-H_{n}-\ln2)}$ 3 Looking for another way to calculate the integral $\iint_{D}{\sin(x)e^{\sin(x)\sin(y)}}\text{d}A$ 2 Is there any theorem connect to this problem? 0 Monotonicity of function $f(x)=(1+\frac1x)^x(1+x)^\frac1x$

### Tags (24)

 7 limits × 2 5 algebra-precalculus 5 calculus × 8 4 integration × 5 5 analysis × 2 4 factorial 5 functions × 2 3 sequences-and-series × 3 5 function-and-relation-composition 2 real-analysis × 2

### Accounts (2)

 Mathematics 358 rep 5 Meta Stack Exchange 101 rep