Math Help - LiMiTs

1. LiMiTs

$\lim_{x\rightarrow1}{\frac{sin3x+sinx-2sin2x}{xsin^2x}}{$

$\lim_{x\rightarrow0}{\frac {sin^{-1}(x)}{x}}$

How Can I solve this?I Tried a lot,and i can't get the answer.

2. Re: LiMiTs

I should split the first limit into three limits. Then use l'Hopital's rule where necessary and for the others try to use some goniometric idenitities to simplify.
For the second one, use l'Hopital's rule.

3. Re: LiMiTs

What is l'Hopital's rule ?

Happy New Year..

4. Re: LiMiTs

Originally Posted by srirahulan
$\lim_{x\rightarrow1}{\frac{sin3x+sinx-2sin2x}{xsin^2x}}$

$\lim_{x\rightarrow0}{\frac {sin^{-1}(x)}{x}}$

Here is the first:
$\lim_{x\rightarrow1}{\frac{sin3x+sinx-2sin2x}{xsin^2x}}=\frac{sin(3)+sin(1)-2sin(2)}{sin^2(1)}}$

5. Re: LiMiTs

For the second limit just try substitution x = sin θ Observe that as x approaches 0, θ also approaches 0