JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let the function \(f(x)=\left\{\begin{array}{cc}\frac{\log _{e}(1+5 x)-\log _{e}(1+\alpha x)}{x} & \text { if } x \neq 0 \\ 10 & \text {; if } x=0\end{array}\right.\) be continuous at \(x=0\).The \(\alpha\) is equal to.
- A \(10\)
- B \(-10\)
- C \(5\)
- D \(-5\)
Answer & Solution
Correct Answer
(D) \(-5\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cc}\frac{\ln (1+5 x)-\ln (1+\alpha x)}{x} & ; x \neq 0 \\ 10 & ; x=0\end{array}\right.\) \(\lim _{x \rightarrow 0} \frac{\ln (1+5 x)-\ln (1+\alpha x)}{x}=10\) Using expension…
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