Basic Calculus: Limits, Continuity, and Derivatives

Which of the following best defines the limit of a function f(x) as x approaches c?

• f(c) is the value of the function at c.

• f(x) gets arbitrarily close to a number L as x approaches c.

• f(x) equals L only when x = c.

• f(x) diverges to infinity as x nears c.

• 9

• 10

• 11

• 12

Which statement best distinguishes the limit of f(x) as x approaches c from the actual value f(c)?

• The limit is always equal to f(c).

• The limit considers only the value at c.

• The limit describes the behavior of f(x) near c, which may differ from f(c).

• f(c) determines the limit.

• 5

• 4

• 2

• Undefined

• 9

• 18

• 27

• 36

• 0

• 2

• 0.5

• 0.25

• The claim is false; the limit depends on the behavior of f(x) near c, not necessarily the value at c.

• The claim is always true.

• The claim is true only for polynomial functions.

• The claim is false; f(c) is always greater than the limit.

• 0

• 0.2

• 1

• 5

Which of the following expressions represents an indeterminate form?

• 0/0

• 1/0

• ∞/0

• 0/1