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Let $f: R \rightarrow R$ be a function such that $\lim _{x \rightarrow \infty} f(x)=M>0$. Then which of the following is false?
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Verified Answer
The correct answer is:
$\lim _{x \rightarrow \infty} x \sin \left(e^{-x}\right) f(x)=M$
$\lim _{x \rightarrow \infty} x \sin \left(e^{-x}\right) f(x)=\lim _{x \rightarrow \infty} \frac{\sin \left(e^{-x}\right)}{e^{-x}} \frac{x}{e^{x}} f(x)$
$=1 \times(0) \times M=0$
$=1 \times(0) \times M=0$
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