Find Limit as x approaches 0 (4sin x+2x)/(5x), if it exists

[calculusqueen]

Find the limit, if it exists.

Limit as x approaches 0 (4sin x+2x)/(5x)

 

[galactus]

Re: Limits

$\displaystyle \lim_{x\to 0}\frac{4sin(x)+2x}{5x}$

Expand it out and make use of the famous limit:

$\displaystyle \lim_{x\to 0}\frac{sin(x)}{x}=1$

We get:

$\displaystyle \frac{4}{5}\lim_{x\to 0}\frac{sin(x)}{x}+\frac{2}{5}$

Now, see it?.