Question:
$\lim _{x \rightarrow 1}\left(\frac{\int_{0}^{(x-1)^{2}} t \cos \left(t^{2}\right) d t}{(x-1) \sin (x-1)}\right)$
Correct Option: , 2
Solution:
$\lim _{x \rightarrow 1} \frac{\frac{1}{2} \sin (x-1)^{4}}{(x-1) \sin (x-1)}$
Let $x-1=h$ when $x \rightarrow 1$ then $h \rightarrow 0$
$\lim _{h \rightarrow 0} \frac{\sin h^{4}}{h^{4}} \times \frac{h}{\sin h} \times h^{2}=1 \times 1 \times 0=0$
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