Find the derivative of $x^x$ using the definition

Evaluate the limit

$\lim_{x\to0}\left(x\cdot\csc\left(3x\right)\right)$

Evaluate the limit

$\lim_{x\to5}\left(\frac{x^2+8x-9}{x^3-x^2+5x-5}\right)$

Evaluate the limit

$\lim_{x\to3}\left(\frac{x^2-1\cdot 8\cdot x+7}{x^3-1\cdot 3\cdot x+2}\right)$

Evaluate the limit

$\lim_{x\to1}\left(\frac{\left(\sqrt{x}\right)^2}{\left(x-1\right)\left(x+1\right)\sqrt{x}+1}\right)$

Evaluate the limit

$\lim_{x\to919191919991}\left(\cos\left(\frac{x}{x}\right)\right)$

Evaluate the limit

$\lim_{x\to1}\left(l\cdot\frac{\ln\left(x\right)}{x-1}\right)$

Evaluate the limit

$\lim_{x\to-2}\left(3x^2-x-10\right)=8$