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, What is indeterminate form? 0/0
lim(x→1) (x³-1)/(x-1) 3
lim(x→0) |x|/x=? dne
limit law: lim(x→c) k=? k
limit law: lim(x→c) x=? c
limit law: lim(x→c) xⁿ=? cⁿ
limit law: lim(x→c) f(x)±g(x)=? lim(x→c) f(x) ± lim(x→c) g(x)
limit law: lim(x→c) f(x)·g(x)=? lim(x→c) f(x) · lim(x→c) g(x)
limit law: lim(x→c) f(x)/g(x)=? 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)=? klim(x→c) f(x)
What are the methods (in priority order) of finding limits? 1. Plug and Chug
2. Factoring
3. Rationalize
4. Complex Fractions
lim(x→π/3) sec(x)=? 2
lim(x→∞) sin(x)=? dne
What are the three reasons why limits do not exist? 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? f(x) is continuous at x=c if lim(x→c) f(x)=f(c).
What are the removable discontinuities? Holes or common factors
What are the nonremovable discontinuities? asymptotes and piecewise functions ( jump discontinuity)
What makes a function left continuous? If lim(x→c⁻) f(x)=f(c).
What makes a function right continuous? If lim(x→c⁺) f(x)=f(c).
What is the vertical asymptote of y=p(x)/q(x)? Where q(x)=0
What is the horizontal asymptote of y=p(x)/q(x) if the there is no horizontal asymptote
degree of p(x) is greater than the degree of q(x)?