JEE Main 2018MathematicsDeterminantsMediumMCQ

JEE Main 2018 — Determinants Question with Solution

JEE Main 2018 (15 Apr)

Question

If fx=cosxx12sinxx22xtanxx1, then limx→0⁡f′xx

Choose an option

Show full solutionCorrect option: B
Correct answer
Bexists and is equal to -2

Step-by-step explanation

Given fx=cosxx12sinxx22xtanxx1

=cosxx2-2x2-2sinxx-x+tanx2x2-x2

=-x2cosx+tanx.x2

=x2tanx-cosx

⇒ Limx→0f'xx=Limx→02xtanx-cosx+x2sec2x+sinxx

=Limx→02tanx-cosx+xsec2x+sinx

=-2

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About this question

This is a previous-year question from JEE Main 2018, covering the Determinants 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.