lim(sqrt(x+1))/(sqrt(4x-1)) as x approaches infinity.

Answer 1

intuitive approach:

as x ---> ∞ √(x+1) --> √x
and √(4x+1) ---> √(4x)

so
lim(√(x+1))/(√(4x-1)) as x ---> ∞
= lim √x/√(4x)
= √(1/4) = 1/2 , as ---> ∞

Answer 2

Thank you! I think I just overwhelmed with the idea of infinity. :)