Question:
The value of $\displaystyle \lim_{y \to \infty} \left[y \, sin \left(\frac{1}{y}\right) - \frac{1}{y} \right]$ is equal to
The value of $\displaystyle \lim_{y \to \infty} \left[y \, sin \left(\frac{1}{y}\right) - \frac{1}{y} \right]$ is equal to
Updated On: Jun 8, 2024
- 1
- $\infty$
- -1
- 0
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The Correct Option is A
Solution and Explanation
$\underset{{y \rightarrow \infty}}{\lim} \left[y \sin \left(\frac{1}{y}\right)-\frac{1}{y}\right]$
$=\underset{{y \rightarrow \infty}}{\lim}\left[\frac{\sin \left(\frac{1}{y}\right)}{\frac{1}{y}}-\frac{1}{y}\right]$
$=1-0=1$
$=\underset{{y \rightarrow \infty}}{\lim}\left[\frac{\sin \left(\frac{1}{y}\right)}{\frac{1}{y}}-\frac{1}{y}\right]$
$=1-0=1$
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Concepts Used:
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Mathematically, a limit is explained as a value that a function approaches as the input, and it produces some value. Limits are essential in calculus and mathematical analysis and are used to define derivatives, integrals, and continuity.
Limits Formula:
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A derivative is referred to the instantaneous rate of change of a quantity with response to the other. It helps to look into the moment-by-moment nature of an amount. The derivative of a function is shown in the below-given formula.
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Read More: Limits and Derivatives