AP Calculus AB full course notes

AP CALCULUS AB
FULL YEAR NOTES 2023-2024
INSTRUCTOR: Condarco



1st 9 weeks

Limits

Direct substitution - go to

● Can’t be used if we get 0 in the denominator
○ Substitute the limit # for x in the equation

Factoring - rationals

● Factor the equation, delete like terms, substitute # for x

Multiplying by conjugate - radicals

● Multiply numerator to fraction so denominator =/= 0, simplify equation, substitute #
for x

Piecewise

● Find left limit (-), find right limit (+)

Combining fractions

● Combine fractions, delete like terms, substitute # for x

Removable discontinuity: hole

Non-removable discontinuity: jump or asymptote




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, Limits at Infinity

Only consider terms with the biggest exponent

Case 1: bigger exponent on bottom

● HA: y=0

Case 2: bigger exponent on top

● slant/oblique asymptote
● Use long division
● Ignore any remainder
○ Slope of slant asymptote pos: infinity=infinity, neg infinity=neg infinity
○ Slope of slant asymptote neg: infinity=neg infinity, neg infinity=infinity

Case 3: exponents are equal

● Divide leading coefficients

Radicals

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● When rational functions have 𝑥 , there are often 2 horizontal asymptotes

IVT-Intermediate Value Theorem

● If f is continuous on [a,b], f(a)=/=f(b), and k is any number in (f(a),f(b)), then there's a
c between (a,b) that equals f(c)=k

Infinite Limits

● Can be infinity, negative infinity, or DNE
○ Use left limit and right limits to solve




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