Calculus check please

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.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  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.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. calculus (help pls)

    Compare the growth rate of the functions f(x) = 4x and g(x) = the square root of the quantity of 16 raised to the x power plus 2 raised to the x power. a. f(x) grows faster than g(x). b. f(x) and g(x) grow at the same rate. c.

  3. Math

    Which of the following functions grows the fastest as x grows without bound? f(x) = x10 g(x) = ln(x10) h(x) = 10x They all grow at the same rate.

  4. Calculus Please Check my answers

    Which of the following functions grows the fastest as x grows without bound? f(x)=x^2 g(x)=x^2+5x

  1. 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

  2. Math

    Which describes the end behavior of the graph of the function f(x)=-2x^3-5x^2+x? a. f(x) approaches infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity b. f(x) approaches negative

  3. Calculus

    Which of the following functions grows the fastest as x goes to infinity? a) f(x) √x b) f(x) √(x+1) c) f(x) √(10x+1) d) They all grow at the same rate as x goes to infinity

  4. 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

  1. 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

  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 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)

  4. 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

View more similar questions or ask a new question.