Find the limit $x\lim_{y\to0}\left(\frac{\sin\left(xy\right)}{yx}\right)$

Find the limit

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

Find the limit

$\lim_{x\to\frac{\pi}{2}}\left(\frac{1-sinx}{1+cos2x}\right)$

Find the limit

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

Find the limit

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

Find the limit

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

Find the limit

$\lim_{x\to1}\left(\frac{9x}{x-1}-\frac{9}{ln\left(x\right)}\right)$

Find the limit

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