JEE Main 2014MathematicsLimitsMediumMCQ

JEE Main 2014 — Limits Question with Solution

JEE Main 2014 (09 Apr Online)

Question

If fx is continuous and f92=29, then limx→0f1-cos3xx2 equals to

Choose an option

Show full solutionCorrect option: C
Correct answer
C 2 9

Step-by-step explanation

Given:  f92=29 and fx is continuous.

limx→0f1-cos3xx2=flimx→01-cos3xx2

=flimx→02sin23x2x2 ∵ 1-cos2θ=2sin2θ

=flimx→02sin23x2493x22

=f92limx→0sin23x23x22

=f92×12     ∵  limx→0sinxx=1

=f92

=29

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About this question

This is a previous-year question from JEE Main 2014, covering the Limits chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.