SOLUTION: I'm not sure if this is under the right label or if calculus can be answered on the site but I'm looking for some help with calculating limits to infinity: calculate the foll

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm not sure if this is under the right label or if calculus can be answered on the site but I'm looking for some help with calculating limits to infinity: calculate the foll      Log On


   

Question 938015: I'm not sure if this is under the right label or if calculus can be answered on the site but I'm looking for some help with calculating limits to infinity:

calculate the following limits, showing all working (steps would be appreciated)
a) lim sqrt 4x^2 - 3/2x + 3
x --> infinity
b) lim sqrt 4x^2 - 3/2x + 3
x --> -infinity

cheers thanks for your time

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I believe you meantlim%28+x-%3Einfinity%2C+%28sqrt%28%284x%5E2+-+3%29%2F%282x+%2B+3%29%29%29%29=
lim(sqrt((4x^2 - 3)/(2x + 3)))
x-->infinity

%284x%5E2+-+3%29%2F%282x+%2B+3%29=2x-3%2B6%2F%282x+%2B+3%29
because lim%28+x-%3Einfinity%2C+%282x%29%29=infinity .
And since lim%28y-%3Einfinity%2C+%28sqrt%28y%29%29%29=infinity ,
with y=%284x%5E2+-+3%29%2F%282x+%2B+3%29=2x-3%2B6%2F%282x+%2B+3%29


lim%28+x-%3E-infinity%2C+%28sqrt%28%284x%5E2+-+3%29%2F%282x+%2B+3%29%29+%29%29 does not exist
because when x%3C-3%2F2 , system%282x%2B3%3C0%2C4x%5E2-3%3E0%29 ---> %284x%5E2+-+3%29%2F%282x+%2B+3%29%3C0 and
sqrt%28%284x%5E2+-+3%29%2F%282x+%2B+3%29%29 does not exist.