Let f:R\toR be a function such that \lim_{x\to\infty} = M > 0. Then which of the following is false?

Correct Answer is : limx→∞xsin(e−x)f(x)=M

\lim_{x\to\infty}x\sin (1/x)f(x)=M

\lim_{x\to\infty}\sin (f(x))=\sin M

\lim_{x\to\infty}x\sin (e^{-x})f(x)=M

\lim_{x\to\infty} {\sin x}/x f(x)=0

KVPY SX SB Exam 2013 Question Paper

Question : 9 of 120

Marks: +1, -0

Let

f : R \to R

be a function such that

\lim↙{x→∞} = M > 0

. Then which of the following is false?

Solution:

\lim↙{x→∞}x\sin (e^{-x})\f(x)

=\lim↙{x→∞}{\sin(e^{-x})}/e^{-x} x/e^x\f(x)

= 1 × (0) × M = 0

Go to Question:

Prev Question

Next Question