`lim_(x->0) sin^-1(x)/x` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply,...

`lim_(x->0) sin^-1(x)/x` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

Expert Answers
Neethu eNotes educator| Certified Educator

Given the limit `lim_{x->0}sin^(-1)(x/x)` . We have to find the limit.

Applying the limit we get,

`lim_{x->0}sin^(-1)(x/x)=lim_{x->0}sin^(-1)(1)=pi/2`

hence the limit is `pi/2`