Find the limit of $\frac{x^2-1}{\sqrt{x}-1}$ as $x$ approaches $1$

Find the limit

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

Find the limit

$\lim_{x\to0}\left(\frac{\sqrt{4+x}-2}{x}\right)$

Find the limit

$\lim_{x\to3}\left(\frac{\sqrt{2x-5}-1}{x-3}\right)$

Find the limit

$\lim_{x\to-3}\left(\frac{x^2+6x+9}{x^2+7x+12}\right)$

Find the limit

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

Find the limit

$\lim_{x\to3}\left(\frac{x^2-9}{x^2-3x}\right)$

Find the limit

$\lim_{x\to1}\left(\frac{x-1}{\sqrt{x+3}-2}\right)$