Question

The function $f$ defined on $\left(-\frac{1}{3}, \frac{1}{3}\right)$ by $f(x) = \left\{ \begin{array}{ll} \frac{1}{x} \log\left(\frac{1+3x}{1-2x}\right) & , x \neq 0 \\> k & , x = 0 \end{array} \right.$ is continuous at $x = 0$, then $k$ is

• A. 6
• B. 1
• C. 5
• D. -5

Hint:

Recall that for a function to be continuous at a point $x=a$, the limit of the function as $x$ approaches $a$ must be equal to the function's value at $a$. Also, remember the standard limit $\lim_{x \to 0} \frac{\log(1+ax)}{ax} = 1$.

Answer 1

The Correct Option is A