Algebra
Integer Answer
MMTS_Full_Test_18
Grade 12
Question:
Let $f(x)=\int_x^{x^2}\dfrac{dt}{\ln t}$. Then $\lim_{x\to1}\dfrac{f(x)}{x-1}$ is
Step-by-Step Solution
Key Concept: L'Hopital or use Leibniz rule as $x\to1$ ($f(1)=0$)
$\lim\frac{f(x)}{x-1}=\lim f'(x)=\lim\frac{x-1}{\ln x}=1$.
Correct Answer: 1