- #1
nietzsche
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- 0
Homework Statement
Find the following limit:
[tex]
\lim_{x \to 0} (1-\text{cos }x)\text{sin }\frac{1}{x}
[/tex]
Homework Equations
The Attempt at a Solution
(1-cos x) -> 0 as x -> 0. sin (1/x) oscillates infinitely many times as x -> 0.
intuition tells me that the limit is 0, but how do i show that?
some ideas i have are using the fact that |sin(1/x)| =< 1, but I'm not sure.