KVPY 2013 - 9

Calculus Level 2

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $\displaystyle\lim_{x\rightarrow\infty}f(x)=M>0$ .

Then which of the following is false ?

Try the whole set KVPY 2013 SB/SX here.

\lim_{x\rightarrow\infty}sin(f(x))=sinM

\lim_{x\rightarrow\infty}xsin(e^{-x})f(x)=M

\lim_{x\rightarrow\infty}xsin(\frac{1}{x})f(x)=M

\lim_{x\rightarrow\infty}\dfrac{sinx}{x}f(x)=0

0 solutions

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