5. Let {xn} and {Yn} be real sequences. (a) Suppose that Xn ~ 0 and Yn ~...

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5. Let {xn} and {Yn} be real sequences.

(a) Suppose that Xn ~ 0 and Yn ~ Q for each n E N. Prove that limsup(xnYn) ~ (limsupxn)(limsuPYn), n--+oo n--+oo n--+oo provided that the product on the right is not of the form 0 . 00. Show by example that this inequality can be strict.

(b) Suppose that Xn ~ 0 ~ Yn for n EN. Prove that provided that none of these products is of the form 0 . 00.

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An Introduction To Analysis

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5. Let {xn} and {Yn} be real sequences. (a) Suppose that Xn ~ 0 and Yn ~...

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An Introduction To Analysis

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