Limit of $\sec \left(\frac{1}{x}\right)$ when $x\to\infty$

Question

Just checking to see if my answer is correct. I am trying to find $\lim\limits_{x \to \infty} \sec\left(\frac{1}{x}\right)$. Is this 1?

Answer 1

Assuming $\sec (1/x) $ instead of $\sec (1/n)$,

$\lim\limits_{x \to \infty} \sec\left(\frac{1}{x}\right)$ = $\lim\limits_{y \to 0^{+}} \sec y = \sec 0 =1$

(Taking $y=1/x $)