[ _x 0 _0^x t ( 10t )dt x] is equal to

Question

$$\mathop {\lim }\limits_{x \to 0} {{\int_0^x {t\sin \left( {10t} \right)dt} } \over x}$$ is equal to

Accepted Answer

$$\mathop {\lim }\limits_{x \to 0} {{\int_0^x {t\sin \left( {10t} \right)dt} } \over x}$$

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

Solutions · 1