Question

Let the function
$f(x)$=$\begin{cases} \frac{\log_e(1+5x) - \log_e(1+\alpha x)}{x}, & \text{if } x ∈ 0 \\\ \space 10 & \text;{if } x = 0 \\\ \end{cases}$
be continuous at x = 0. Then α is equal to

• A. 10
• B. -10
• C. 5
• D. -5

Answer 1

Answer: (D)

-5

Answer 2

It_{{x \to 0}}$$\frac{(1+5x)-In(1+αx)}{x}
⇒5–α=10
⇒ α=−5
So, the correct option is (D): -5