AP Calculus BC: Multiple Choice Test Review UPDATED ACTUAL Exam Questions and CORRECT Answers

AP Calculus BC: Multiple Choice Test
Review UPDATED ACTUAL Exam
Questions and CORRECT Answers
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).



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