Evaluate {lim}_{x\to0} {xtanx}/(1-cosx)

NIMCET 2017 Question Paper with solutions

Question : 120 of 120

Marks: +1, -0

Evaluate

{lim}↙{x→0}

{xtanx}/(1-cosx)

Solution:

It is clear that function is of the form

0/0

therefore by using L'Hopital rule.
=

\lim↙{x→0}

{xsex^2x+tanx}/{sinx}

Again apply L’ Hopital rule,
=

\lim↙{x→0}

{x(2sec^2xtanx+sex^2x+sex^2x)}/{cosx}

Putting x = 0, we get

\lim↙{x→0}

f (x) = 2

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