Question

The limit of the following series as x approaches $\frac{\pi }{2}$ is
$f\left(x\right)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+.....$

• A. $\frac{2\pi }{3}$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{3}$
• D. 1

Answer 1

The correct option is D 1

$f\left(x\right)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}...$
$f\left(x\right)=sinx$
${lim}_{x\to \frac{\pi }{2}}f\left(x\right)={lim}_{x\to \frac{\pi }{2}}sinx=1$