if f(x) = {1 if x < 1, x if 1< x }and g(x) ={x if x ≠ 2, 3 if x = 2} Evalute a. lim x→0 g(x)/f(x) b. lim x→2 f(x)/g(x)

Question

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Answer 1

a) As x→0, f(x)=1, g(x)→0 so g(x)/f(x)→0

b) As x→2, f(x)→2, g(x)→2 because x is either less than 2 or greater than 2, so x≠2, and f(x)/g(x)→2/2 so f(x)/g(x)→1 (not ⅔)