Lim x approaches infinity of (Square root of x^2 + 2) / x-1 ... ?

Question

Mathematics

Jaida Sloan

16 August, 03:57

Lim x approaches infinity of (Square root of x^2 + 2) / x-1 ... ?

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Answers (1)

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Raison · Answer 1

The answer is

lim sqrt (x^2 + 2) / x - 1 = lim sqrt [x^2 (1 + 2 / x^2) / x - 1 =

lim x sqrt [ (1 + 2 / x^2) / x (1 - 1/x) = lim sqrt [ (1 + 2 / x^2) / (1 - 1/x)

and when x approaches infinity we have

lim sqrt (x^2 + 2) / x - 1 = sqrt [ (1 + 0) / (1 - 0) = 1/1 = 1