# How do you find lim (1-cosx)/x as x->0 using l'Hospital's Rule?

Dec 15, 2016

$0$

#### Explanation:

Note that we're in indeterminate form ($\frac{0}{0}$), so we can use l'Hospital's Rule.

L'hospital's Rule states that ${\lim}_{x \to c} \frac{g \left(x\right)}{h \left(x\right)} = {\lim}_{x \to c} \frac{g ' \left(x\right)}{h ' \left(x\right)}$.

Therefore:

${\lim}_{x \to 0} \frac{1 - \cos x}{x}$

$= {\lim}_{x \to 0} \frac{\left(1 - \cos x\right) '}{x '}$

$= {\lim}_{x \to 0} \frac{\sin x}{1}$

$= \sin \frac{0}{1}$

$= 0$

Hopefully this helps!