# LiMiTs

• December 31st 2012, 07:13 AM
srirahulan
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.
• December 31st 2012, 08:03 AM
Siron
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.
• December 31st 2012, 02:45 PM
srirahulan
Re: LiMiTs
What is l'Hopital's rule ?

Happy New Year..
• December 31st 2012, 03:01 PM
Plato
Re: LiMiTs
Quote:

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:
$\lim_{x\rightarrow1}{\frac{sin3x+sinx-2sin2x}{xsin^2x}}=\frac{sin(3)+sin(1)-2sin(2)}{sin^2(1)}}$
• January 1st 2013, 12:11 AM
ibdutt
Re: LiMiTs
For the second limit just try substitution x = sin θ Observe that as x approaches 0, θ also approaches 0