Question

The value of $\underset{y\to \infty }{\lim }\left[ysin\left(\frac{1}{y}\right)-\frac{1}{y}\right]$ is equal to

• A. 1
• B. $\infty$
• C. - 1
• D. 0
• E. $-\infty$

Answer 1

Answer: (A)

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