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# Let f RR be a function. Suppose a, b are two real numbers such that for any sequence (xi) with xia for all i and lim x = a, lim f(x) = b. Prove that lim f(x) = b.

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## Let f RR be a function. Suppose a, b are two real numbers such that for any sequence (xi) with xia for all i and lim x₁ = a, lim f(x) = b. Prove that lim f(x) = b. (Hint: do a proof by i4x x-a contradiction. Suppose lim f(x) #b, then there exists >0 such that...) x→a

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**Related Book For**

## Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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