Question

Assertion :When $|x|<1,\underset{n\to \infty }{lim}\frac{\log (x+2)-x^{2n}cosx}{x^{2n}+1}=\log (x+2)$. Reason: For $-1<x<1$, as $n\to \infty ,x^{2n}\to 0$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let $L=\underset{n\to \infty }{lim}\frac{\log (x+2)-x^{2n}\cos x}{x^{2n}+1}$
Given $|x|<1\Rightarrow |x{|}^{2n}$ as $x\to \infty$ is $=0$
Hence required limit is, $L=\frac{\log (x+2)-0.\cos x}{0+1}=\log (x+2)$
Clearly both the statement are correct and Reason is correctly explaining Assertion.