Question

Find: Lim x->0 (x^2 * cos(1/x^2))

Answer 1

I know that x^2 will make f(x) = 0 but when you find the limit of cos(1/x^2), thats cos(infinity) which should be undefined. In that case would the answer be there is no limit?

Answer 2

squeeze theorem

Answer 3

\[-1\le \cos(x)\le1\]
\[-1\le\cos\left(\frac{1}{x^2}\right)\le 1\]
\[-x^2\le x^2\cos\left(\frac{1}{x^2}\right)\le x^2\]

Answer 4

Limit is 0