Question

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 g(x) as x goes to infinity.
- g(x) grows faster than f(x) as x goes to infinity. (my answer)
- f(x) and g(x) grow at the same rate as x goes to infinity.
- The rate of growth cannot be determined.

3. What does lim 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 infinity. (my answer)
- f(x) grows faster than g(x) as x goes to infinity.
- L'Hôpital's Rule must be used to determine the true limit value.

4. Which of the following functions grows at the same rate as 3x as x goes to infinity?
- 2x
- √3^x+4
- √6^x (my answer)
- √9^x+5

5. Which of the following functions grows the slowest as x goes to infinity?

- 5^x
- 5^x (my answer)
- x^5
- They all grow at the same rate.

Answer 1

#1. 3>e, so 3^x grows faster than e^x
#2. I don't like any of the choices. How does 1 relate to 1+cosx?
#3. Since the limit f/g = limit f'/g', f grows faster
#4 assuming you meant 3^x rather than 3x, then you want D.
#5 ?? A and B are the same.