Limits of cos and sin?

Question

1) limit x appr 0 cos(7/x) ?
2) limit x appr 0 (x^2)/sin^2(3x)

Answer 1

2).

Multiply nominator and denominator by 9.

Limit formulas:

Answer 2

1).

Lim     [cos (7/x)]

x → 0

The limit does not exists.

Because, cos(7/0) = cos(∞), the cosine function is periodic and keeps oscillating while approaching ∞.

So, the limit is undetermined.