Question

lim as x-> infinity sec^2(1/x)

Answer 1

As x ---> ∞ , 1/x ---> 0

So
lim sec^2(1/x) as x---> infinity
= lim sec^2(x) as x---> 0
= lim (1/cos^2(x) as x --->0
= 1/1
= 1