Calculus

Which of the following functions grows at the same rate as 3^x as x goes to infinity?

a)2^x
b)sqrt(3^(x)+4)
c)sqrt(6^x)
d)sqrt(9^(x)+5^(x))

I tried this, but I'm not sure how to deal with the square roots when using l'hopital's rule. I don't think the answer is 2^x because you'd have the limit as x approaches infinity of 3^x/2^x. This can be made into (3/2)^x, so 1.5^infinity is infinity meaning they don't grow at the same rate. Can someone help me with setting up the square roots with l'hopital's rule?

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  1. well, 3=√9, so 3^x = √(9^x) = √(9^x)
    So, as x gets large, 5^x is zero compared to 9^x, so it can be ignored, just as with polynomials, lower powers can be ignored.
    So, pick (D)

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