28 How can I calculate the derivative of $g(z)=\int_{z^2}^{z^3}\frac{1}{\sqrt{1+t^2}} dt$? 18 Find a limit without l'Hospital: $\lim_{x\to -\infty}\left(\frac{\ln(2^x + 1)}{\ln(3^x+ 1)}\right)$ 14 What is the result of $\lim_{x\to0_+} \frac{e^x - x e^x - 1}{\left(e^x - 1 \right)^2}$ without L'Hôpital's rule. 14 Looking for series that suits 1,1,-1,-1,1,1,-1,-1 .. 11 partial derivative of an integral function

### Reputation (58,819)

 +10 Condition necessary and sufficient in order a function to be periodic -2 Finding the asymptotes of the trajectory of a point parameterized by $(x,y)=\left(\frac{t}{1-t^2},\frac{t-2t^3}{1-t^2}\right)$ for $t\geq 0$ +25 $\lim_{n \to \infty} a_n = \infty$ iff $\{a_n\}$ is not bounded above +10 Solve $f'=\sqrt{|1-f|}$

### Questions (31)

 5 How to compute $\int_0^{\frac{\pi}{2}}\frac{\arctan(\sqrt{\tan(x)})}{\tan(x)}dx$ 5 Prove if $\lim_{x\to +\infty}(f(x)+f'(x))=0$ then $\lim_{x\to +\infty} f(x)=0$ [duplicate] 4 find the limit of the sum $\sum_{k=n}^{2n-1}\frac{1}{2k+1}$ 4 Is it possible to find the expression of the antiderivative $\int \frac{dx}{\cosh(x)+\sqrt{\cosh(2x)}}$ 3 No rational has a square of the form $\frac 1t-t$ where $t$ is a rational in $(0,1)$

### Tags (365)

 1k calculus × 930 260 convergence-divergence × 218 868 real-analysis × 766 243 algebra-precalculus × 224 681 limits × 503 223 functions × 199 623 sequences-and-series × 497 223 trigonometry × 177 504 integration × 362 213 analysis × 143

### Bookmarks (16)

 26 $f(f(x)f(y))+f(x+y)=f(xy)$ 6 Let $f:\mathbb{R}\to(0,\infty)$ be a differentiable function. For all $x\in\mathbb{R}$ $f'(x)=f(f(x)).$ Then show that such function does not exists [duplicate] 3 Proof for dense and closed 3 Generating primitive Pythagorean triples 2 Evaluating $\lim_{x\to 0} \frac{x^2}{e^x-1}$