How do you evaluate the limit (sin^2(3x)/(sin(x^2)) as x approaches 0?

2 Answers
Somebody N.
Mar 15, 2018

See other answer.

Ratnaker Mehta
Mar 15, 2018

# 9#.

Explanation:

#lim_(x to 0)sin^2(3x)/sin(x^2)#,

#=lim{(sin3x)/(3x)*3x}^2-:{sin(x^2)/x^2*x^2}#,

#=lim{(9x^2-:x^2)}[{(sin3x)/(3x)}^2-:{sin(x^2)/x^2}]#.

Since, #lim_(theta to 0)sintheta/theta=1#, we have,

#"The Reqd. Lim.="(9)(1^2-:1)=9#.

Related questions
Impact of this question
734 views around the world
You can reuse this answer
Creative Commons License