Question

Limits!
Evaluate using the squeeze theorem.
lim x^2 cos 1/x
x->0

Help!! I have a lot of these to do so details would be uber helpful

Answer 1

\(\cos\theta\) is always between -1 and 1, regardless of what \(\theta\) is. This means that\[x^2\le |x^2\cos\theta|\]

Answer 2

sorry, I meant that\[|x^2\cos\theta|\le x^2\]

Answer 3

therefore we can write\[-x^2\le x^2\cos(\frac1x)\le x^2\]