Question

The value of $\displaystyle \lim_{y \to \infty} \left[y \, sin \left(\frac{1}{y}\right) - \frac{1}{y} \right]$ is equal to

• A. 1
• B. $\infty$
• C. -1
• D. 0

Answer 1

Answer: (A)

1

Answer 2

$\underset{{y \rightarrow \infty}}{\lim} \left[y \sin \left(\frac{1}{y}\right)-\frac{1}{y}\right]$
$=\underset{{y \rightarrow \infty}}{\lim}\left[\frac{\sin \left(\frac{1}{y}\right)}{\frac{1}{y}}-\frac{1}{y}\right]$
$=1-0=1$