Calculus Examples

$lim_{x \to \infty} \sin (\frac{1}{x})$

Step 1

Move the limit inside the trig function because sine is continuous.

$\sin (lim_{x \to \infty} \frac{1}{x})$

Step 2

Since its numerator approaches a real number while its denominator is unbounded, the fraction $\frac{1}{x}$ approaches $0$ .

$\sin (0)$

Step 3

The exact value of $\sin (0)$ is $0$ .

$0$