I'm trying to work out this problem:
Let $f(x) = x cos x$. Prove that for every number $\epsilon > 0$, the following statement is true:
$If 0 < | x - 0 | < \epsilon$ then $|f(x) - 0 < \epsilon|$
This is my attempt:
Suppose $0 < |x - 0| < \epsilon$. We know that $$|f(x) - 0| = |x cos x| = |x||cos x|$$ Since $$|x| < \epsilon $$
$$|x||cos x| < \epsilon |cos x|$$
Now I'm unable to proceed from here and stuck. How should this problem be approcached ?