# 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?

1. 👍
2. 👎
3. 👁
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)

1. 👍
2. 👎

## Similar Questions

1. ### Help me check my calculus answers

1. Which of the following functions grows the fastest as x goes to infinity? - 2^x - 3^x - e^x inf f(x)/g(x) = 5 show? - g(x) grows faster than f(x) as x goes to infinity. - f(x) and g(x) grow at the same rate as x goes to

2. ### Calculus

Compare the rates of growth of f(x) = x + sinx and g(x) = x as x approaches infinity. f(x) grows faster than g(x) as x goes to infinity. g(x) grows faster than f(x) as x goes to infinity. f(x) and g(x) grow at the same rate as x

3. ### Calculus

Which of the following functions grows the fastest as x goes to infinity? (2 points) f(x) = ln(x) f(x) = log2(x) f(x) = x2 f(x) = 2x

4. ### Calculus

Which of the following functions grows at the same rate as e^x as x goes to infinity? a) e^(x+3) b) e^(3x) c) e^(2x) d) e^(-x)

1. Which of the following functions grows the fastest as x goes to infinity? - 2^x - 3^x - e^x (my answer) - x^20 2. Compare the rates of growth of f(x) = x + sinx and g(x) = x as x approaches infinity. - f(x) grows faster than

2. ### Algebra

which of the following functions has a rate of change that stays the same??/ A y= -4x + 10 B y= 1/2 x^2 C y= 3^x D y= x^2 + 2

3. ### calculus

Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5. Which of the following statement is true? (it's a positive

4. ### Calculus

What does lim x-->∞ f(x)/g(x)=0 show? a) g(x) grows faster than f(x) as x goes to infinity b) f(g) and g(x) grow at the same rate as x goes to infinity c) f(x) grows faster than g(x) as x goes to infinity d) LHopital's Rule must

1. ### Calculus

Which of the following functions grows the slowest as x goes to infinity? x^e e^x ex they all grow the same rate. I think it is c because it does not have any exponents.