A) \[\infty \]
B) \[-\infty \]
C) 0
D) \[\frac{3}{4}\]
Correct Answer: C
Solution :
We have, \[g\left( x \right)=\int_{0}^{\left| x \right|3/4}{{{\left( t \right)}^{2/3}}\sin \left( \frac{1}{t} \right)dt}\] |
\[g'\left( x \right)={{\left| x \right|}^{\frac{1}{2}}}\sin \frac{1}{{{\left| x \right|}^{3/4}}}_{x\to 0}^{\lim }\frac{g\left( x \right)}{x}\] |
\[_{x\to 0}^{\lim }\frac{g'\left( x \right)}{1}=_{x\to 0}^{\lim }{{\left| x \right|}^{1/2}}\sin \frac{1}{{{\left| x \right|}^{3/4}}}=0\] |
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