11. What is the limit of a function at a point where the function is defined but not continuous?
A) The limit does not exist
B) The limit is equal to the function's value at that point
C) The limit is always zero
D) The limit is infinite
12. What is the limit of a function as x approaches a point where the function has a jump discontinuity?
A) The limit is equal to the jump size
B) The limit does not exist
C) The limit is always zero
D) The limit is infinite
13. Which of the following statements is true about the Intermediate Value Theorem?
A) It guarantees the existence of a limit for all functions
B) It states that a continuous function takes on every value between any two points
C) It is used to find vertical asymptotes of functions
D) It only applies to differentiable functions
14. What type of discontinuity occurs when a function approaches different values from the left and right at a point?
A) Removable discontinuity
B) Infinite discontinuity
C) Jump discontinuity
D) Oscillating discontinuity
15. Which of the following functions is not continuous at x = 0?
A) f(x) = x^2
B) g(x) = 1/x
C) h(x) = |x|
D) k(x) = sin(x)
16. What is the limit of the function f(x) = 1/x as x approaches infinity?
A) The limit does not exist
B) The limit is 0
C) The limit is 1
D) The limit is infinity
17. What is the limit of the function f(x) = sin(x)/x as x approaches 0?
A) The limit does not exist
B) The limit is 0
C) The limit is 1
D) The limit is infinity
18. Which of the following is a condition for a function to be continuous on a closed interval [a, b]?
A) The function is differentiable at every point in the interval
B) The function has no vertical asymptotes in the interval
C) The function is defined at every point in the interval
D) The limit of the function exists at every point in the interval
19. What is the limit of the function f(x) = x^2 - 4x + 4 as x approaches 2?
A) 0
B) 2
C) 4
D) 8
20. Which of the following functions is continuous for all real numbers?
A) f(x) = 1/x
B) g(x) = x^2
C) h(x) = |x|
D) k(x) = sin(x)
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