$$\mathop {\lim }\limits_{x \to 0} {{\int_0^x {t\sin \left( {10t} \right)dt} } \over x}$$ is equal to
JEE · Math · previous-year question
- A.$$ - {1 \over 5}$$
- B.$$ - {1 \over 10}$$
- C.0correct
- D.$$ {1 \over 10}$$
Answer
C. 0
Explanation
$$\mathop {\lim }\limits_{x \to 0} {{\int_0^x {t\sin \left( {10t} \right)dt} } \over x}$$ This is in $${0 \over 0}$$ form. So apply newton leibniz rule $$\mathop {\lim }\limits_{x \to 0} {{x.\sin \left( {10x} \right) - 0} \over 1}$$ = 0
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