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 25 How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? 25 Calculus proof for the area of a circle 17 How to compute $\sqrt{i + 1}$ 13 Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$ 9 Formula for the sequence repeating twice each power of $2$

### Reputation (8,657)

 +10 Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$ +10 proving $\csc^2 \left( \frac{\pi}{7}\right)+\csc^2 \left( \frac{2\pi}{7}\right)+\csc^2 \left( \frac{4\pi}{7}\right)=8$ +10 Complex analysis - Trigonometric conjugate +10 How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

### Questions (48)

 28 Evaluate:: $2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right)$ 12 Curl of a vector in spherical coordinates 11 How to solve an exponential equation with two different bases: $3^x - 2^x = 5$ 9 how to evaluate $\int_0^\infty e^{- \left ( x - \frac a x \right )^2} dx$ 9 how to find this limit $\lim_{x\rightarrow 0} \frac{\sin x^2}{ \ln ( \cos x^2 \cos x + \sin x^2 \sin x)} = -2$ without using L'Hôpital's rule

### Tags (104)

 210 calculus × 87 58 definite-integrals × 16 132 integration × 59 52 trigonometry × 12 122 limits × 40 36 inequality × 11 86 sequences-and-series × 36 35 complex-analysis × 20 63 real-analysis × 40 33 limits-without-lhopital × 2

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