Find the limit of $\frac{x^2-4}{3-\sqrt{x+7}}$ as $x$ approaches $2$

Find the limit

$\lim_{x\to0}\left(\frac{2^x-3^x}{x}\right)$

Find the limit

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

Find the limit

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

Find the limit

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

Find the limit

$\lim_{x\to3}\left(\frac{x^2-9}{x^2-5x+6}\right)$

Find the limit

$\lim_{x\to0}\left(\frac{1-\cos\left(x^2\right)}{x^2}\right)$

Find the limit

$\lim_{x\to0}\left(\frac{\cos\left(5x\right)-1}{x^2}\right)$