Simplify the expression $\frac{x^5+2x^3-x-8}{x^2-2x+1}$

Evaluate the limit

$\lim_{x\to0}\left(\left(1-e^x\right)^{\frac{1}{\ln\left(x\right)}}\right)$

Evaluate the limit

$\lim_{x\to0}\left(arcsin\left(x\right)\right)^{\tan\left(x\right)}$

Evaluate the limit

$\lim_{x\to1}\left(\tan\left(\frac{\pi x}{4}\right)^{\tan\left(\frac{\pi x}{2}\right)}\right)$

Evaluate the limit

$\lim\:_{x\to\:1}\left(1+3\cdot\:\:lnx\right)^{\left(\frac{1}{sen\:\left(1-x\right)}\right)}$

Evaluate the limit

$\lim_{x\to0}\left(x+\sin\left(x\right)\right)^{\tan\left(x\right)}$

Evaluate the limit

$\lim_{x\to1}\left(x^{\tan\left(\pi \frac{1}{2}\cdot x\right)}\right)$

Evaluate the limit

$\lim_{x\to0}\left(x^x\right)$