Question

For what value of $k$, the function defined by $f(x) = \begin{cases} \frac{log(1+2x)sin\,x^\circ}{x^2} & \text{for } x \ge \text {0}\\\ k & \text{for } x = \text{ 0} \end{cases}$ is continuous at $x = 0$ ?

• A. $2$
• B. $\frac{1}{2}$
• C. $\frac{\pi}{90}$
• D. $\frac{90}{\pi}$

Answer 1

Answer: (C)

$\frac{\pi}{90}$

Answer 2

Given, p(x) = \begin{cases} \frac{log (1+2x) sin \,x^{\circ}}{x^{2}} & \text{for x \neq 0} \\\[2ex] k, & \text{forx=0 } \end{cases}