TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow \infty} x\left(\log \left(1+\frac{x}{2}\right)-\log \frac{x}{2}\right)=\)
- A 0
- B 1
- C 2
- D e
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{x \rightarrow \infty} x\left[\log \left(1+\frac{x}{2}\right)-\log \frac{x}{2}\right] \\ & =\lim _{x \rightarrow \infty} x\left[\frac{\log \left(1+\frac{x}{2}\right)}{\frac{x}{2}}\right]\left\{\because \log a-\log b=\log \frac{a}{b}\right\} \\ & =\lim _{x…
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