Range of the function $f(x) = \frac{2x}{x^{2}+1}$
123674
Show that $y = \frac{2x}{x^2 +1}$ lies between $-1$ and $1$ inclusive.
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
119469
Find the limit of $\lim\limits_{(x,y)\to (0,0)} \frac{x^2y^2}{x^2y^2+(x-y)^2}$
87489
Find range of $f(x)=3|\sin x|-4|\cos x|$
61486
Show that $f$ is not differentiable at $(0,0)$ - $\frac{x_1^2x_2}{x_1^2+x_2^2}$
63750
let $f(\frac{x}{3})+f(\frac{2}{x})=\frac{4}{x^2}+\frac{x^2}{9}-2$ then find $f(x)$
31931
limit as $x$ approaches infinity of $\frac{1}{x}$
158888
Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$.
136297
Evaluate $\lim_{x \to 1} \frac{\sqrt[3]{x} -1}{\sqrt{x} -1}$
127558
If $f(x)=x-\int^{\frac{\pi}{2}}_0f(x)\sin(x)dx$ find the explicit function for $f(x)$ in its simplest form
145496
Show $\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$ Proof verification
88432
A problem on range of a trigonometric function: what is the range of $\frac{\sqrt{3}\sin x}{2+\cos x}$?
27969
Why does $\frac{1}{x} < 4$ have two answers?
72769
How find this function $xf(x^2)=f(x),x>0$
85535
Finding maximum of $|f'(i)|$
52858
Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
10068
$f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.