Calc BC Chapter 1: Limits and Continuity
UPDATED ACTUAL Exam Questions and
CORRECT Answers
differential calculus - CORRECT ANSWER - calculus arising from the tangent line problem
integral calculus - CORRECT ANSWER - calculus arising from the area problem
two-sided limit - CORRECT ANSWER - requires the values of f(x) to get closer and closer to
L as values of x are taken from either side of x = a
one-sided limit - CORRECT ANSWER - when the function exhibits different behaviors on the
left and right sides of x = a
the relationship between one-sided and two-sided limits - CORRECT ANSWER - if the one-
sided limits from the left and right sides of a are equal then L is the same for the two-sided limit
infinite limits - CORRECT ANSWER - when x approaches a, f(x) increases or decreases
without bound
vertical asymptotes - CORRECT ANSWER - they illustrate one-sided or two-sided infinite
limits in a function
basic limits - CORRECT ANSWER - lim k = k
x -> a
lim x = a
x -> a
lim (1/x) = -infinity
x -> 0 (left)
, lim (1/x) = +infinity
x -> 0 (right)
Limit Properties (same for one-sided limits) - CORRECT ANSWER - a. The limit of a sum is
the sum of the limits.
b. The limit of a difference is the difference of the limits.
c. The limit of a product is the product of the limits.
d. The limit of a quotient is the quotient of the limits, provided the limit of the denominator isn't
zero.
e. The limit of an nth root is the nth root of the limit.
Limit of Polynomials Theorem - CORRECT ANSWER - For p(x) = c0 + c1x^1 + ... + cnx^n,
lim p(x) = c0 + c1a + ... + can^n = p(a)
x -> a
indeterminate form of type 0/0 - CORRECT ANSWER - a quotient f(x)/g(x) in which the
numerator and denominator both have a limit of zero as x -> a
Limits of Rational Functions Theorem - CORRECT ANSWER - Let f(x) = p(x)/q(x) be a
rational function, and let a be any real number. If q(a) =/= 0, then lim f(x) = f(a).
x -> a
If q(a) = 0 but p(a) =/= 0, then lim f(x) = DNE
x -> a
limits of piecewise functions - CORRECT ANSWER - the two-sided limits of these functions
are found by first finding the one-sided limits
end behavior - CORRECT ANSWER - the behavior of a function f(x) as x increases or
decreases without bound (limits at infinity)
UPDATED ACTUAL Exam Questions and
CORRECT Answers
differential calculus - CORRECT ANSWER - calculus arising from the tangent line problem
integral calculus - CORRECT ANSWER - calculus arising from the area problem
two-sided limit - CORRECT ANSWER - requires the values of f(x) to get closer and closer to
L as values of x are taken from either side of x = a
one-sided limit - CORRECT ANSWER - when the function exhibits different behaviors on the
left and right sides of x = a
the relationship between one-sided and two-sided limits - CORRECT ANSWER - if the one-
sided limits from the left and right sides of a are equal then L is the same for the two-sided limit
infinite limits - CORRECT ANSWER - when x approaches a, f(x) increases or decreases
without bound
vertical asymptotes - CORRECT ANSWER - they illustrate one-sided or two-sided infinite
limits in a function
basic limits - CORRECT ANSWER - lim k = k
x -> a
lim x = a
x -> a
lim (1/x) = -infinity
x -> 0 (left)
, lim (1/x) = +infinity
x -> 0 (right)
Limit Properties (same for one-sided limits) - CORRECT ANSWER - a. The limit of a sum is
the sum of the limits.
b. The limit of a difference is the difference of the limits.
c. The limit of a product is the product of the limits.
d. The limit of a quotient is the quotient of the limits, provided the limit of the denominator isn't
zero.
e. The limit of an nth root is the nth root of the limit.
Limit of Polynomials Theorem - CORRECT ANSWER - For p(x) = c0 + c1x^1 + ... + cnx^n,
lim p(x) = c0 + c1a + ... + can^n = p(a)
x -> a
indeterminate form of type 0/0 - CORRECT ANSWER - a quotient f(x)/g(x) in which the
numerator and denominator both have a limit of zero as x -> a
Limits of Rational Functions Theorem - CORRECT ANSWER - Let f(x) = p(x)/q(x) be a
rational function, and let a be any real number. If q(a) =/= 0, then lim f(x) = f(a).
x -> a
If q(a) = 0 but p(a) =/= 0, then lim f(x) = DNE
x -> a
limits of piecewise functions - CORRECT ANSWER - the two-sided limits of these functions
are found by first finding the one-sided limits
end behavior - CORRECT ANSWER - the behavior of a function f(x) as x increases or
decreases without bound (limits at infinity)
