AP Calculus BC Multiple Choice Test Review – Study Guide, Practice Questions &
Exam Prep
What is a limit? - correct answer ✔✔A y-value that x approaches as you move along the graph
Write: the limit as x approaches a of the function of x is equal to L - correct answer ✔✔lim(x→a)
f(x)=L
lim (x→-2) (x³+8)/(x+2)=? - correct answer ✔✔12
T/F: The point doesn't have to exist for the limit to exist - correct answer ✔✔T
What is a left sided limit? What is its notation? - correct answer ✔✔A limit that x approaches
from the right side of the graph: lim(x→a⁻) f(x)=L
What is a right sided limit? What is its notation? - correct answer ✔✔A limit that x approaches
from the right side of the graph: lim(x→a⁺) f(x)=L
Draw the graph f(x){x+2: x>3, -x+5: x<3
Using this graph, what is lim(x→3⁻) f(x)? What is lim(x→3⁺) f(x)? lim(x→3) f(x)? - correct answer
✔✔lim(x→3⁻) f(x)=2
lim(x→3⁺) f(x)=5
lim(x→3) f(x)=dne
What does dne stand for? - correct answer ✔✔does not exist
Draw the graph f(x)=x/(x-2)
,Using this graph, what is lim(x→2⁻) f(x)? What is lim(x→2⁺) f(x)? lim(x→2) f(x)? - correct answer
✔✔lim(x→2⁻) f(x)=-∞
lim(x→2⁺) f(x)=∞
lim(x→2) f(x)=dne
Draw the graph -log(|x|)
Using this graph, what is lim(x→0) f(x)? - correct answer ✔✔lim(x→0) f(x)=∞
What is indeterminate form? - correct answer ✔✔0/0
lim(x→1) (x³-1)/(x-1) - correct answer ✔✔3
lim(x→0) |x|/x=? - correct answer ✔✔dne
limit law: lim(x→c) k=? - correct answer ✔✔k
limit law: lim(x→c) x=? - correct answer ✔✔c
limit law: lim(x→c) xⁿ=? - correct answer ✔✔cⁿ
limit law: lim(x→c) f(x)±g(x)=? - correct answer ✔✔lim(x→c) f(x) ± lim(x→c) g(x)
limit law: lim(x→c) f(x)·g(x)=? - correct answer ✔✔lim(x→c) f(x) · lim(x→c) g(x)
limit law: lim(x→c) f(x)/g(x)=? - correct answer ✔✔lim(x→c) f(x)/lim(x→c) g(x), g(x)≠0, lim(x→c)
g(x)≠0
, limit law: lim(x→c) kf(x)=? - correct answer ✔✔klim(x→c) f(x)
What are the methods (in priority order) of finding limits? - correct answer ✔✔1. Plug and Chug
2. Factoring
3. Rationalize
4. Complex Fractions
lim(x→π/3) sec(x)=? - correct answer ✔✔2
lim(x→∞) sin(x)=? - correct answer ✔✔dne
What are the three reasons why limits do not exist? - correct answer ✔✔1. Infinite Osculation
2. Increases/Decreases without bound
3. The limit from the right does not equal the limit from the left
What is the calculus definition of continuity? - correct answer ✔✔f(x) is continuous at x=c if
lim(x→c) f(x)=f(c).
What are the removable discontinuities? - correct answer ✔✔Holes or common factors
What are the nonremovable discontinuities? - correct answer ✔✔asymptotes and piecewise
functions (jump discontinuity)
What makes a function left continuous? - correct answer ✔✔If lim(x→c⁻) f(x)=f(c).
What makes a function right continuous? - correct answer ✔✔If lim(x→c⁺) f(x)=f(c).
Exam Prep
What is a limit? - correct answer ✔✔A y-value that x approaches as you move along the graph
Write: the limit as x approaches a of the function of x is equal to L - correct answer ✔✔lim(x→a)
f(x)=L
lim (x→-2) (x³+8)/(x+2)=? - correct answer ✔✔12
T/F: The point doesn't have to exist for the limit to exist - correct answer ✔✔T
What is a left sided limit? What is its notation? - correct answer ✔✔A limit that x approaches
from the right side of the graph: lim(x→a⁻) f(x)=L
What is a right sided limit? What is its notation? - correct answer ✔✔A limit that x approaches
from the right side of the graph: lim(x→a⁺) f(x)=L
Draw the graph f(x){x+2: x>3, -x+5: x<3
Using this graph, what is lim(x→3⁻) f(x)? What is lim(x→3⁺) f(x)? lim(x→3) f(x)? - correct answer
✔✔lim(x→3⁻) f(x)=2
lim(x→3⁺) f(x)=5
lim(x→3) f(x)=dne
What does dne stand for? - correct answer ✔✔does not exist
Draw the graph f(x)=x/(x-2)
,Using this graph, what is lim(x→2⁻) f(x)? What is lim(x→2⁺) f(x)? lim(x→2) f(x)? - correct answer
✔✔lim(x→2⁻) f(x)=-∞
lim(x→2⁺) f(x)=∞
lim(x→2) f(x)=dne
Draw the graph -log(|x|)
Using this graph, what is lim(x→0) f(x)? - correct answer ✔✔lim(x→0) f(x)=∞
What is indeterminate form? - correct answer ✔✔0/0
lim(x→1) (x³-1)/(x-1) - correct answer ✔✔3
lim(x→0) |x|/x=? - correct answer ✔✔dne
limit law: lim(x→c) k=? - correct answer ✔✔k
limit law: lim(x→c) x=? - correct answer ✔✔c
limit law: lim(x→c) xⁿ=? - correct answer ✔✔cⁿ
limit law: lim(x→c) f(x)±g(x)=? - correct answer ✔✔lim(x→c) f(x) ± lim(x→c) g(x)
limit law: lim(x→c) f(x)·g(x)=? - correct answer ✔✔lim(x→c) f(x) · lim(x→c) g(x)
limit law: lim(x→c) f(x)/g(x)=? - correct answer ✔✔lim(x→c) f(x)/lim(x→c) g(x), g(x)≠0, lim(x→c)
g(x)≠0
, limit law: lim(x→c) kf(x)=? - correct answer ✔✔klim(x→c) f(x)
What are the methods (in priority order) of finding limits? - correct answer ✔✔1. Plug and Chug
2. Factoring
3. Rationalize
4. Complex Fractions
lim(x→π/3) sec(x)=? - correct answer ✔✔2
lim(x→∞) sin(x)=? - correct answer ✔✔dne
What are the three reasons why limits do not exist? - correct answer ✔✔1. Infinite Osculation
2. Increases/Decreases without bound
3. The limit from the right does not equal the limit from the left
What is the calculus definition of continuity? - correct answer ✔✔f(x) is continuous at x=c if
lim(x→c) f(x)=f(c).
What are the removable discontinuities? - correct answer ✔✔Holes or common factors
What are the nonremovable discontinuities? - correct answer ✔✔asymptotes and piecewise
functions (jump discontinuity)
What makes a function left continuous? - correct answer ✔✔If lim(x→c⁻) f(x)=f(c).
What makes a function right continuous? - correct answer ✔✔If lim(x→c⁺) f(x)=f(c).
