Help with Limits Homework: Evaluate sqrt(tan3x)+sqrt(sin2x)/sqrt(tan2x)

[EL ALEM]

Homework Statement

evaluate the lim as x->0 of [sqroot(tan3x)+srroot(sin2x)]/sqroot(tan2x) WITHOUT using L'Hospital's Rule
Answer is sqrt3/2 + 1

This is in the exam review for my class, and I am having a hard time getting started on this one. Thanks in advance.

Homework Equations

The Attempt at a Solution

 

[lanedance]

i would divide it into 2 separate limits & try some trig angle sum indentities

 

[EL ALEM]

thanks! ill try it out.

 

[EL ALEM]

ok tried it, but I am having trouble b/c of the sqr root

 

[lanedance]

$$\lim_{x\to 0} \frac{\sqrt{tan3x}+\sqrt{sin2x}}{\sqrt{tan2x}} = \lim_{x\to 0} \left \sqrt{\frac{tan3x}{tan2x}} +\sqrt{\frac{sin2x}{tan2x}}$$

so all the operations should be within the sqrt's