Question: 1. Using definitions (rather than limit theorems) Prove that lim f(x) x--+a+ exists and equals L in each of the following cases. (a) f(x) =

1. Using definitions (rather than limit theorems) Prove that lim f(x)

x--+a+

exists and equals L in each of the following cases.

(a) f(x) = lxi/x, a = 0, and L = 1.

(b) f(x) = -l/x, a = 0, and L = -00.

(c) f(x) = (x - 1)/(x2 + X - 2), a = -2, and L = 00.

(d) f(x) = 1/(x2 - 1), a = 1, and L = 00.

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