Find the limit of $\frac{\sin\left(x-1\right)}{x-1}$ as $x$ approaches $1$

Find the limit

$\lim_{x\to0}\left(\frac{e^{2x}-e^{-2x}-4x}{x-sin\left(x\right)}\right)$

Find the limit

$\lim_{x\to0}\left(\frac{1}{x}-\frac{1}{sin\left(x\right)}\right)$

Find the limit

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

Find the limit

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

Find the limit

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

Find the limit

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

Find the limit

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