What is the limit of (2x^2 + 1)^0.5 / (3x -5) as x goes to infinity?

1 Answer
A. S. Adikesavan
Apr 23, 2016

sqrt 2/3.

Explanation:

As xtooo, 1/x and 1/x^2to0.

The given expression is ((x^2(2+1/x^2))^0.5)/(x(3-5/x))
=(((x^2)^0.5)((2+1/x^2)^0.5))/((x(3-5/x))
=(x(2+1/x^2)^0.5)/(x(3-5/x)
=((2+1/x^2)^0.5)/(3-5/x).

As, xtooo, 1/x^2 and 1/xto0 and the given expression to2^0.5/3=sqrt 2/3

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