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Prove that $ \displaystyle \lim_{x \to 0}x^4 \cos \frac{2}{x} = 0 $.

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Campbell University

Harvey Mudd College

University of Nottingham

Boston College

We have a question in this we need to prove that limit X approaches to zero. Access to the power four cost to buy stocks exit is really powerful because to buy X equal to zero, we have to prove it. So this could be done as limit X approaches to zero x rays to depart for In two. Cause I'm sorry and to limit X approaches to zero of course to buy X no cost to works. So for any value of this two by X, any value of two works cause will always be within the range minus one 21 So we can write it as limit X approaches to zero. X raised to the power for anything would win -1: one. Come on. This equal to 0, 0 into minus 121. So this will become zero, which is our right inside and improved. Thank you.