Question

$\int \left[{lim}_{h\to 0}\frac{sec(x+h)-secx}{h}\right]dx=$

• A. $secx+c$
• B. $-secx+c$
• C. $secxtanx+c$
• D. $-secxtanx+c$

Answer 1

The correct option is A $secx+c$

$\int \left[{Lim}_{h\to 0}\frac{sec(x+h)-secx}{h}\right]dx$

${Lim}_{h\to 0}\frac{f(x+h)-f\left(x\right)}{h}=\frac{df\left(x\right)}{dx}$

$\Rightarrow \int \frac{dsecx}{dx}dx$

$\Rightarrow secx+c$