If the function f defined on (-13,13) by f(x)=cases1x_e(1+3x1-2x), & x0, & x=0cases is con…

Question

If the function $f$ defined on $\left(-\dfrac13,\dfrac13ight)$ by $f(x)=\begin{cases}\dfrac1x\log_e\left(\dfrac{1+3x}{1-2x}ight), & x
e0\k, & x=0\end{cases}$ is continuous, then $k$ is equal to \_\_\_\_\_\_\_.

Answer: 5

Accepted Answer

$$\lim_{x\to0}\frac{\ln(1+3x)}{3x}\cdot3-\frac{\ln(1-2x)}{-2x}\cdot(-2)=3+2=5\Rightarrow k=5$$

Solutions · 1