• 0

• f(a)

• Does not exist

• Undefined

• The integral of f(x)

• The derivative of f(x)

• The value that f(x) approaches as x tends to infinity

• The value that x approaches infinity

• f(x) is differentiable at a

• the left-hand and right-hand limits exist but are not equal

• f(x) is continuous only at a

• the left-hand and right-hand limits exist and are equal

What is the condition for the continuity of a function at a specific point?

• f(x) is continuous at x = a if the left-hand limit equals the right-hand limit.

• f(x) is continuous at x = a if f(x) is defined at x = a.

• f(x) is continuous at x = a if the limit of f(x) as x approaches a is equal to f(a).

• f(x) is continuous at x = a if f(x) is bounded around x = a.

f(x) is differentiable at x = a if ____.

• the limit lim(x -> a) (f(x)-f(a))/(x-a) exists

• f(x) is continuous at x = a and has a maximum value

• f(x) is defined at x = a with no breaks in the graph

• f(x) is differentiable at every point in the neighborhood of a

L'hôpital's Rule states that if the limit of a function f(x)/g(x) gives an indeterminate form 0/0 or ∞/∞, then the limit can be evaluated by differentiating both numerator and denominator.

• Multiplying the numerator and the denominator by conjugates gives the limit.

• Differentiating the numerator and the denominator gives the limit.

• Using integration on the numerator and denominator gives the limit.

• Substituting values directly into f(x) and g(x) gives the limit.

• lim₍ₕ→0₎ [(f(a+h) - f(a))/h]

• lim₍ₓ→a₎ [(f(x) - f(a))/(x - a)]

• lim₍ₕ→0₎ [(f(h) - f(a))/h]

• lim₍ₓ→0₎ [(f(a+x) - f(a))/a]

• lim as h → 0 of (f(x+h) - f(x)) / h

• lim as x → 0 of (f(x+h) - f(x)) / h

• lim as h → 0 of (f(x) - f(x+h)) / h

• lim as h → 0 of (f(x+h) + f(x)) / h

• 1

• c

• undefined

• 0