47 How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? 43 Calculus proof for the area of a circle 23 Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$ 19 How to compute $\sqrt{i + 1}$ 10 How prove this inequality

### Reputation (9,634)

 +10 Finding the angle of rotation of an ellipse from its general equation and the other way around +10 Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$ +10 dotting gradient in spherical coordinates with displacement vector +5 How to show that $1 \over \sqrt{1 - 4x}$ generate $\sum_{n=0}^\infty \binom{2n}{n}x^n$

### Questions (63)

 33 Evaluate:: $2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right)$ 13 Curl of a vector in spherical coordinates 11 How to solve an exponential equation with two different bases: $3^x - 2^x = 5$ 10 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 10 Evaluate: $\sum_{n=1}^{\infty}\frac{1}{n k^n}$

### Tags (121)

 260 calculus × 86 70 definite-integrals × 16 146 integration × 59 66 real-analysis × 41 144 limits × 39 59 limits-without-lhopital × 3 89 sequences-and-series × 36 47 proof-explanation 74 trigonometry × 12 43 circles