### Questions (8)

 62 Why can't the second fundamental theorem of calculus be proved in just two lines? 11 Tricky inequality involving 3 variables 6 Proving $n^2 \csc^2(nx) = \sum_{k=0}^{n-1}\csc^2\left(x+ k \frac{\pi}{n}\right)$ (without calculus?) 6 How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$? 5 Is the Epsilon-Delta definition of a limit not precise enough?

### Reputation (502)

 +15 Proving $n^2 \csc^2(nx) = \sum_{k=0}^{n-1}\csc^2\left(x+ k \frac{\pi}{n}\right)$ (without calculus?) +15 Why can't the second fundamental theorem of calculus be proved in just two lines? +5 In the MacLaurin series of $\ln(1+x)$, why must $x$ lie in $(-1,1]$? +5 How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$?

### Answer (1)

 0 Finding out the period of function $f(x+2)=\frac{f(x)-5}{f(x)-3}$

### Tags (14)

 0 inequality × 2 0 definite-integrals 0 determinant 0 trigonometry 0 real-analysis 0 taylor-expansion 0 infinitesimals 0 a.m.-g.m.-inequality 0 calculus 0 radicals

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