Question

How do you find `lim sinx/x` as `x->0` using l'Hospital's Rule?

Answer 1

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

Explanation:

`lim_(x->0) sinx/x` is a well known standard limit `=1`.

Here, we are asked to use l'Hospital's rule since the limit reduces to the indeterminate form `0/0`

Thus, `lim_(x->0) sinx/x = lim_(x->0) (d/dx sinx)/(d/dx x)`

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