AP Calc BC Unit 1.1 - Limits and Continuity

f(x) us continuous at x=a if and only if:

1. f(a) is defined

2. left and right limits of f(x) as x→a match

3. lim f(x) as x→a = f(a)

Intermediate Value Theorem

A continuous function cannot skip values

1. Only keep terms with biggest exponents

2. plug in (big) or (-big) for x

3. can either be ∞, -∞, or a fraction if top and bottom have same exponent

1. Multiply top and bottom by a*b

2. Do not cancel yet, distribute side that had fraction originally

3. Factor both sides and cancel

4. Plug in limit

Negative Exponent

put in denominator

Fraction Exponent

root, denominator becomes the root