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AP Calculus BC Multiple Choice Test Review Questions and Answers
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AP Calculus BC Multiple Choice Test Review Questions and Answers What is a limit? - 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 - Answer-lim(x→a) f(x)=L /.lim (x→-2) (x³+8)/(x+2)=? - Answer-12...

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  • January 26, 2025
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  • 2024/2025
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AP Calculus BC Multiple Choice Test Review
Questions and Answers

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

/.lim (x→-2) (x³+8)/(x+2)=? - Answer-12

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

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

/.What does dne stand for? - 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)? -
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)? - Answer-lim(x→0) f(x)=∞

/.What is indeterminate form? - Answer-0/0

/.lim(x→1) (x³-1)/(x-1) - Answer-3

/.lim(x→0) |x|/x=? - Answer-dne

/.limit law: lim(x→c) k=? - Answer-k

/.limit law: lim(x→c) x=? - Answer-c

, /.limit law: lim(x→c) xⁿ=? - Answer-cⁿ

/.limit law: lim(x→c) f(x)±g(x)=? - Answer-lim(x→c) f(x) ± lim(x→c) g(x)

/.limit law: lim(x→c) f(x)·g(x)=? - Answer-lim(x→c) f(x) · lim(x→c) g(x)

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

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

/.lim(x→π/3) sec(x)=? - Answer-2

/.lim(x→∞) sin(x)=? - Answer-dne

/.What are the three reasons why limits do not exist? - 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? - Answer-f(x) is continuous at x=c if
lim(x→c) f(x)=f(c).

/.What are the removable discontinuities? - Answer-Holes or common factors

/.What are the nonremovable discontinuities? - Answer-asymptotes and piecewise
functions (jump discontinuity)

/.What makes a function left continuous? - Answer-If lim(x→c⁻) f(x)=f(c).

/.What makes a function right continuous? - Answer-If lim(x→c⁺) f(x)=f(c).

/.What is the vertical asymptote of y=p(x)/q(x)? - Answer-Where q(x)=0

/.What is the horizontal asymptote of y=p(x)/q(x) if the degree of p(x) is greater than the
degree of q(x)? - Answer-there is no horizontal asymptote

/.What is the horizontal asymptote of y=p(x)/q(x) if the degree of p(x) is less than the
degree of q(x)? - Answer-y=0

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