Can you help me with solving this limit?

[deuxillusion]

Find the limit as x approaches zero for the following function.
f(x)= 5x + 5x cos(5x)
_____________
sin(5x)cos(5x)

so far I've rewritten this as 1/(sin(5x)/5x) * (1/(cos(5x) +1) but when I use the trig properties for finding limits i'm messing something up... how would you solve this problem from here? (assuming it's right so far..)

 

[daon2]

You have it right.

Let \(\displaystyle u = 5x\), note that \(\displaystyle x\to 0 \implies u\to 0\) then rewrite:

\(\displaystyle \displaystyle \frac{u + u\cos u}{\sin u \cos u} = (\sec u+1) \frac{u}{\sin u}\)

 

[deuxillusion]

thank you!