# medicu

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 6 Calculate the limit of $nx_n^2$ 6 What is $\lim_{x\to0} \frac{(\cos x + \cos 2x + \dots+ \cos nx - n)}{\sin x^2}$? 5 Finding determinant using properties of determinant without expanding 5 Find lim:$\lim_{x\to0} \frac{\tan(\tan x) - \sin(\sin x)}{\tan x -\sin x}$ 5 What is the result of $\lim_{n \to \infty} \frac{ \sum^n_{i=1} i^k}{n^{k+1}},\ k \in \mathbb{R}$ and why?

# 1,933 Reputation

 +20 $a_{n+1}=1+\frac{1}{a_n}.$ Find the limit. +45 Number theory: $x^y + 1 = y^x$ +15 Prove $\log_ab+\log_bc+\log_ca\geq1+\log_{ab}bc+\log_{bc}ab$ +10 Find the possible values of |A + B + C |

# 27 Questions

 13 Prove or disprove the implication: 6 How to prove the equality $\int^{na}_{ma}\frac{\ln(x-a)}{x^2+a^2}\,dx = \int^{\frac{a}{m}}_{\frac{a}{n}}\frac{\ln(x+a)}{x^2+a^2}\,dx$? 5 What explains this bizarre behavior? 5 Intersection of $\{ [n\sqrt{2}]\mid n \in \mathbb{N}^* \}$ and $\{ [n(2+\sqrt{2})]\mid n \in \mathbb{N}^* \}$ 5 Solve equation $1+2^x=3^y$

# 53 Tags

 57 limits × 37 9 real-analysis × 11 46 calculus × 33 8 definite-integrals × 8 19 integration × 18 6 diophantine-equations × 5 13 sequences-and-series × 18 6 matrices × 2 11 algebra-precalculus × 12 5 elementary-number-theory × 5

# 1 Account

 Mathematics 1,933 rep 311