1. Which of the following functions grows the fastest as x goes to infinity?

Question

- 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.
- 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 <-- my answer
- √6^x
- √9^x+5

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

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

Answer 1

see

https://www.jiskha.com/display.cgi?id=1530619883