KVPY SX SB Exam 19-Nov-2017 Question Paper

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Question : 86 of 120

Marks: +1, -0

Let

g(x) =∫ ↖{|x|^{2 \/ 4} }↙{0}t^{2 \/ 3}\sin1/tdt

, for all real x.
Then

\lim↙{x→0}{g(x)}/x

is equal to

∞
–∞
0
$3/4$

Solution:

Apply L hospital rule

g'(x) = {|x|^{1 \/ 2} } \sin({1/ {|x|^{3 \/ 4} } )

\lim↙{x→0}{g'(X)}

\lim↙{x→0}|x|^{1 \/ 2} \sin({1/ {|x|^{3 \/ 4} })=0

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