here is the question : find upper and lower bound of the function $$f(x)=cos(\frac{1}{x})$$ Domain of function is all Real numbers except {1} . I tried to solve it by finding the limits of $f(x)$ as $x$ approaches both from negative and positive. But, $$lim_{x\rightarrow 0} cos(\frac{1}{x})$$ (from negative or positive) is undefined as far as I know. Show me any hint please. Thank You!
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You mean, you want to find bounds of possible values of function? – openspace Dec 30 '15 at 23:22
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6Hint: $-1\le\cos t\le1$ – egreg Dec 30 '15 at 23:37