Question

If limₓtₒᵢₙfty xsin((1)/(x))=A and limₓ\to0 xsin((1)/(x))=B, then which one of the following is correct?

• A. \(A=1,\;B=0\)
• B. \(A=0,\;B=1\)
• C. \(A=0,\;B=0\)
• D. A=1,B=1

Hint:

Use standard limits: sin t ~ t as t\to0.

Answer 1

The Correct Option is A

As x→∞, sin(1/x)~ 1/x, hence A=1. As x\to0, xsin(1/x)→ 0 by squeeze theorem, hence B=0.