Question

$\underset{h\to 0}{\mathrm{Lim}}\frac{\underset{a}{\overset{x+h}{\int }}{\ln }^{2}tdt-\underset{a}{\overset{x}{\int }}{\ln }^{2}tdt}{h}=$

• A. 0
• B. ${\ln }^{2}x$
• C. $\frac{2\ln x}{x}$
• D. does not exist

Answer 1

Answer: (B)

Differentiating w.r.t. h
$\underset{h\to 0}{\mathrm{Lim}}\frac{{\ln }^2(x+h)-{\ln }^2(a)\cdot 0-0}{1}={\ln }^{2}x$