Question: Suppose that g : R R is differentiable and that g'(x) > 1 for all x R. Prove that if g(l) = 0

Suppose that g : R → R is differentiable and that g'(x) > 1 for all x ∈ R. Prove that if g(l) = 0 and f(x, y) = (x - l)2(y + l)/(yg(x)), then there is an L ∈ R such that f(x, y) → L as (x, y) (1, b) for all b ∈ R\{0}.

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