Calculate the limit as x goes to infinity of ((4x^4+9x)^.5-2x^2)

Question

This should be equal to zero, but i can't quite get it. Please help. I really to figure this out soon. Thanks!!!

Answer 1

This can be written: sqrt(4x^4(1+9x/4x^4))-2x^2=2x^2sqrt(1+9/4x^3)-2x^2=2x^2(sqrt(1+9/4x^3)-1). As x gets large the square root gets closer to 1, so the contents of the brackets approaches zero and the whole expression therefore approaches zero.