what is lim_x-0x(e^x-1)/1-cosx

\lim_{x \to 0} \frac{x (e^{x} - 1)}{1 - \cos x} S o i t o f \frac{0}{0} f o r m, s o a p p l y L - h o s p i t a l r u l e, u n t i l t h i s f o r m i s r e m o v e d . S o \frac{x (e^{x} - 1)}{1 - \cos x} = \frac{\frac{d}{d x} (x e^{x} - x)}{\frac{d}{d x} (1 - \cos x)} = \frac{e^{x} + x e^{x} - 1}{\sin x}, t h i s i s s t i l l \frac{0}{0} f o r m, S o a p p l y a g a i n H e n c e \frac{\frac{d}{d x} (e^{x} + x e^{x} - 1)}{\frac{d}{d x} (\sin x)} = \frac{e^{x} + e^{x} + x e^{x}}{\cos x}, t h i s i s n o t \frac{0}{0} f o r m, s o p u t x = 0 H e n c e \lim_{x \to 0} \frac{x (e^{x} - 1)}{1 - \cos x} = \frac{1 + 1 + 0}{1} = 2 (a n s)

what is limx-0x(ex-1)/1-cosx