Question

How do you find `lim sin(2x)/x` as `x->0` using l'Hospital's Rule?

Answer 1

`lim_(x->0) sin(2x)/x = 2`

Explanation:

The limit:

`lim_(x->0) sin(2x)/x` is in the indeterminate form `0/0` so we can solve it using l'Hospital's rule:

`lim_(x->0) sin(2x)/x = lim_(x->0) (d/dx sin(2x))/(d/dx x) = lim_(x->0) (2cos(2x))/1 = 2`