Evaluate the limit?

Question

Evaluate the limit

lim
x--> Infinity

√9+10x^2 / (7+9x)

Answer 1

sqrt(9+10x^2) = ixI* sqrt(9/x^2+10)
so your limit is Ix I/x * sqrt(9/x^2+10)/(9+7/x)
the second factor ==> sqrt10/9 and the first is 1 for x==> +infinity and -1 for x==> -infinity
so you have two limits 1/9 sqrt10 for x ==>+ infinity and
-1/9sqrt(10) for nx==>-infinity