# How do you find the limit of #(x+sin x ) / ( 3x + cosx )# as x approaches infinity using l'hospital's rule?

##### 1 Answer

The limit

#### Explanation:

L'Hospital's rule states the that:

if

The same also applies for indeterminate form of

So we can differentiate the top of the fraction and the bottom of the fraction and then try to evaluate the limit again.

So:

and

So from l'hospital's rule we can say that:

We can say that

Doing a graph of the function we can see that the graph oscillates around

graph{(x+sin(x))/(3x+cos(x)) [-0.82, 9.18, -2.66, 2.34]}