HELP!!! find the limit as x approaches infinity...?

Question

lim as x approaches infinity of sqrt(x^2+4)/sqrt(4x^2+1)?

Answer 1

the answer is 1/2.. what you do is you divide the numerator and the denominator by sqrt(x^2), for the numertor, you get sqrt(1+4/(x^2)) and for the denominator you get sqrt(4+1/(x^2)) so with that, you're left with sqrt(1) over sqrt(4), which is 1/2

Answer 2

The answer is 1/2 because dividing the top and bottom by x^2 gives a fraction that tends to 1/4 as x tends to infinity and the sq root of 1/4 is 1/2

Answer 3

as x approaches infinity
the denominator, sqrt(4x^2+1), also approaches infinity
therfore the result approaches 0

Answer 4

Take the derivative of the numerator and denominator and apply L'Hospitals Rule.

Doug