medicu

 10 Find lim:$\lim_{x\to0} \frac{\tan(\tan x) - \sin(\sin x)}{\tan x -\sin x}$ 6 How to prove $\lim_{n\to\infty}\sum_{k=1}^{n}\frac{n+k}{n^2+k}=\frac{3}{2}$? 6 Number theory: $x^y + 1 = y^x$ 6 Calculate the limit of $nx_n^2$ 6 What is $\lim_{x\to0} \frac{(\cos x + \cos 2x + \dots+ \cos nx - n)}{\sin x^2}$?

### Reputation (3,070)

 +5 How to calculate the integral $\int_{0}^{1}e^{\arctan x}\,dx$? +5 The sequence $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}, x_0>0$ is bounded? +5 Solve equation $1+2^x=3^y$ +15 Arc length of logarithm function

### Questions (51)

 14 Constant sequence? 13 Prove or disprove the implication: 9 The sequence $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}, x_0>0$ is bounded? 7 Solve equation $1+2^x=3^y$ 6 What is the maximum of numbers?

### Tags (69)

 86 limits × 42 12 real-analysis × 12 66 calculus × 41 11 definite-integrals × 10 26 integration × 21 9 diophantine-equations × 8 20 sequences-and-series × 21 7 inequality × 15 15 algebra-precalculus × 15 7 problem-solving × 3

### Account (1)

 Mathematics 3,070 rep 99 silver badges1414 bronze badges