- #1
fire9132
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Homework Statement
Evaluate using the Squeeze Theorem.
[itex] \lim_{x\rightarrow0} (2^{x} - 1) cos\frac{1}{x} [/itex]
Homework Equations
The Attempt at a Solution
[itex] -1 ≤ cos\frac{1}{x} ≤ 1 \\
1 - 2^{x} ≤ (2^{x} -1)cos\frac{1}{x} ≤ 2^{x} - 1 \\
0 ≤ (2^{x} -1)cos\frac{1}{x} ≤ 0 \\
∴ \lim_{x\rightarrow0} (2^{x} - 1) cos\frac{1}{x} = 0 [/itex]
That's the solution I got and the solution that's in my textbook. But when I checked on wolframalpha, it says the limit does not exist.
Did I do something wrong and is my textbook wrong? or is it something conceptually that I don't understand about this? Is wolframalpha wrong?
Thanks :)