AP Calculus BC Multiple Choice Test Review Questions and Answers

AP Calculus BC: Multiple Choice Test
Review

What is a limit? - Correct Answers -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 Answers -
lim(x→a) f(x)=L

lim (x→-2) (x³+8)/(x+2)=? - Correct Answers -12

T/F: The point doesn't have to exist for the limit to exist - Correct Answers -T

What is a left sided limit? What is its notation? - Correct Answers -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 Answers -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 Answers -lim(x→3⁻) f(x)=2
lim(x→3⁺) f(x)=5
lim(x→3) f(x)=dne

What does dne stand for? - Correct Answers -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 Answers -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 Answers -lim(x→0) f(x)=∞

What is the second derivative of a parametric function? - Correct Answers
-d²y/dx²=[d/dt(dy/dx)]/(dx/dt)

x=t²-4
y=t/2

, d²y/dx²=? - Correct Answers -d²y/dx²=-1/8t³

x=t³-9t
y=t²
Find the equation of the tangent line at (0, 9). - Correct Answers -y-9=(1/3)x
y-9=(-1/3)x

c(t)=⟨t², (1/2)t⟩
Find v(t), a(t), and speed at t=1. - Correct Answers -v(t)=⟨2, 1/2⟩
a(t)=⟨2, 0⟩
|v(t)|=√17/2

What is x in polar form? - Correct Answers -x=rcosθ

What is indeterminate form? - Correct Answers -0/0

lim(x→1) (x³-1)/(x-1) - Correct Answers -3

lim(x→0) |x|/x=? - Correct Answers -dne

limit law: lim(x→c) k=? - Correct Answers -k

limit law: lim(x→c) x=? - Correct Answers -c

limit law: lim(x→c) xⁿ=? - Correct Answers -cⁿ

limit law: lim(x→c) f(x)±g(x)=? - Correct Answers -lim(x→c) f(x) ± lim(x→c) g(x)

limit law: lim(x→c) f(x)·g(x)=? - Correct Answers -lim(x→c) f(x) · lim(x→c) g(x)

limit law: lim(x→c) f(x)/g(x)=? - Correct Answers -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 Answers -klim(x→c) f(x)

What are the methods (in priority order) of finding limits? - Correct Answers -1. Plug and
Chug
2. Factoring
3. Rationalize
4. Complex Fractions

lim(x→π/3) sec(x)=? - Correct Answers -2

lim(x→∞) sin(x)=? - Correct Answers -dne