L\lim_(n \to \0) (sin x)/(x)

Question

L
`\lim_(n \to \0) (sin x)/(x)`

Answer 1

1

Explanation:

`\displaystyle \lim_(x \to 0)(\sin x)/(x)`

Let

`f(x)= \sin x`

`g(x)=x`

We are going to use L'Hopital's Rule here that states

`\displaystyle \lim_(x \to c)(f(x))/(g(x))=\lim_(x \to c)(f'(x))/(g'(x))`

We know that

`f'(x) = \cos x` and
`g'(x)=1`

so

`\displaystyle \lim_(x \to 0)(\sin x)/(x)=\lim_(x \to 0)(\cos x)/(1)=1`