Question

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

Answer 1

`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`