Limits of Exponential Functions Flashcards
(24 cards)
What is the limit of the exponential function f(x) = e^x as x approaches infinity?
The limit is infinity.
True or False: The limit of e^x as x approaches negative infinity is 0.
True.
Fill in the blank: The limit of the function f(x) = a^x as x approaches negative infinity is ____ when a > 1.
0.
What is the general behavior of exponential functions as x approaches positive infinity?
They grow without bound (approach infinity).
For the function f(x) = 2^x, what is the limit as x approaches 0?
The limit is 1.
What is the limit of f(x) = 3^(-x) as x approaches infinity?
The limit is 0.
Multiple Choice: Which of the following limits is correct? A) lim (x -> 0) e^x = 0 B) lim (x -> 0) e^x = 1 C) lim (x -> 0) e^x = ∞
B) lim (x -> 0) e^x = 1.
What is the limit of f(x) = 5^x as x approaches negative infinity?
The limit is 0.
True or False: The function f(x) = a^x is continuous for all real x.
True.
What is the limit of f(x) = e^(1/x) as x approaches 0 from the right?
The limit is infinity.
Fill in the blank: The limit of the function f(x) = a^x as x approaches positive infinity is ____ when a > 1.
∞.
What happens to the limit of the function f(x) = a^x as x approaches negative infinity when 0 < a < 1?
The limit approaches infinity.
Multiple Choice: Which limit is true for f(x) = e^(-x)? A) lim (x -> ∞) e^(-x) = 0 B) lim (x -> ∞) e^(-x) = ∞ C) lim (x -> ∞) e^(-x) = 1
A) lim (x -> ∞) e^(-x) = 0.
What is the limit of f(x) = 4^x as x approaches negative infinity?
The limit is 0.
True or False: The limit of e^(x^2) as x approaches infinity is infinity.
True.
Fill in the blank: The limit of f(x) = a^(-x) as x approaches positive infinity is ____ when a > 1.
0.
What is the limit of f(x) = (1/2)^x as x approaches infinity?
The limit is 0.
Multiple Choice: What is the limit of f(x) = e^(x) as x approaches negative infinity? A) 0 B) 1 C) ∞
A) 0.
What is the limit of f(x) = 10^x as x approaches negative infinity?
The limit is 0.
True or False: The exponential function f(x) = 2^x has a horizontal asymptote at y = 0.
True.
What is the limit of f(x) = 7^(-x) as x approaches infinity?
The limit is 0.
Fill in the blank: For any a > 1, the limit of a^x as x approaches negative infinity is ____.
0.
What is the limit of f(x) = e^(x) as x approaches 0?
The limit is 1.
Multiple Choice: Which of the following statements is true? A) The limit of e^(x) as x approaches -∞ is 1 B) The limit of e^(x) as x approaches ∞ is 0 C) The limit of e^(x) as x approaches -∞ is 0
C) The limit of e^(x) as x approaches -∞ is 0.
