Calculus Examples

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

Step 1

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

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

Step 2

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

$\cos (0)$

Step 3

The exact value of $\cos (0)$ is $1$ .

$1$