AP Calculus BC: Multiple Choice Test Review Exam

What is a limit? - ANS 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 - ANS lim(x→a) f(x)=L lim (x→-2) (x³+8)/(x+2)=? - ANS 12 T/F: The point doesn't have to exist for the limit to exist - ANS T What is a left sided limit? What is its notation? - ANS 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? - ANS 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: x3, -x+5: x3 Using this graph, what is lim(x→3⁻) f(x)? What is lim(x→3⁺) f(x)? lim(x→3) f(x)? - ANS lim(x→3⁻) f(x)=2 lim(x→3⁺) f(x)=5 lim(x→3) f(x)=dne What does dne stand for? - ANS 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)? - ANS 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)? - ANS lim(x→0) f(x)=∞ What is indeterminate form? - ANS 0/0 lim(x→1) (x³-1)/(x-1) - ANS 3 lim(x→0) |x|/x=? - ANS dne limit law: lim(x→c) k=? - ANS k limit law: lim(x→c) x=? - ANS c limit law: lim(x→c) xⁿ=? - ANS cⁿ limit law: lim(x→c) f(x)±g(x)=? - ANS lim(x→c) f(x) ± lim(x→c) g(x) limit law: lim(x→c) f(x)·g(x)=? - ANS lim(x→c) f(x) · lim(x→c) g(x) limit law: lim(x→c) f(x)/g(x)=? - ANS 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)=? - ANS klim(x→c) f(x) What are the methods (in priority order) of finding limits? - ANS 1. Plug and Chug 2. Factoring 3. Rationalize 4. Complex Fractions lim(x→π/3) sec(x)=? - ANS 2 lim(x→∞) sin(x)=? - ANS dne What are the three reasons why limits do not exist? - ANS 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? - ANS f(x) is continuous at x=c if lim(x→c) f(x)=f(c). What are the removable discontinuities? - ANS Holes or common factors What are the nonremovable discontinuities? - ANS asymptotes and piecewise functions (jump discontinuity) What makes a function left continuous? - ANS If lim(x→c⁻) f(x)=f(c). What makes a function right continuous? - ANS If lim(x→c⁺) f(x)=f(c). What is the vertical asymptote of y=p(x)/q(x)? - ANS 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)? - ANS 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)? - ANS y=0 What is the horizontal asymptote of y=p(x)/q(x) if the degree of p(x) is equal to the degree of q(x)? - ANS the ratio of the leading coefficients How do you determine a vertical asymptote from a limit? - ANS If lim(x→L⁻) f(x)=±∞ or lim(x→L⁺) f(x)=±∞, then x=L is the vertical asymptote of f(x) How do you determine a horizontal asymptote from a limit? - ANS If lim(x→±∞) f(x)=L, then x=L is the horizontal asymptote of f(x) lim(x→∞) (5+x)/(x²-1)=? - ANS 0 lim(x→-∞) (2x²+1)/(x-3)=? - ANS -∞ lim(x→∞) (5x-7)/(2x+3)=? - ANS 5/2 lim(x→2⁻) (4x+1)/(x-2)=? - ANS -∞