Stuck on Calculus question! HELP!

[mathiscool05]

I've been stuck on this question for a while now. I've typed the question into a limits calculator and the answer comes up as 1/sqrt 2 but i don't understand how to get that.

lim (sqrt 2x^2 +3x - sqrt 2x^2 +x)
x > infinity

 

[HallsofIvy]

It's difficult to read this without parentheses. Do you mean sqrt(2x^2- 3x)- sqrt(2x^2+ x)? If so, multiply by the fraction \(\displaystyle \frac{\sqrt{2x^2- 3x}+ \sqrt{2x^2+ x}}{\sqrt{2x^2- 3x}+ \sqrt{2x^2+ x}}\)

 

[richardt]

Greetings:

Assuming that you meant to parenthesize the arguments 2x^2 + 3x and 2x^2 + x, you can multiply the entire expression by (1/x) / (1/x) for an indeterminate expression of the form 0/0 and, accordingly, one which is eligible for L'Hopital.

Rich