Question

please give me prove for this one. thanks. ​

Answer 1

Answer:

1

Step-by-step explanation:

We cannot substitute $0$ in place of $x$ in the denominator because dividing by $0$ is undefined. We need to use L'Hôpital's rule.

By rewriting the limit by taking the derivatives of the numerator and denominator, we get $\lim_{x\to0} \dfrac{\dfrac{d \sin{x}}{dx}}{\dfrac{dx}{dx}}$

$\lim_{x\to0} \dfrac{\cos{x}}{1}$

$\cos{0} = 1$