Question

How do you find the limit `lim_(x->0)sin(x)/x` ?

Answer 1

We will use l'Hôpital's Rule.

l'Hôpital's rule states:

`lim_(x->a) f(x)/g(x) = lim_(x->a) (f'(x))/(g'(x))`

In this example, `f(x)` would be `sinx`, and `g(x)` would be `x`.

Thus,

`lim_(x->0) (sinx)/x = lim_(x->0) (cosx)/(1)`

Quite clearly, this limit evaluates to `1`, since `cos 0` is equal to `1`.