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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