RATES OF CHANGE AND LIMITS Mrs. Erickson Limits and Continuity The concept of a limit is one of the ideas that distinguishes calculus from algebra and.

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Rates of Change and LimitsMrs. Erickson

Limits and ContinuityThe concept of a limit is one of the ideas that distinguishes calculus from algebra and trig. One of the uses of limits is to test for continuity.

Limits and ContinuityRates of Change and Limits:Averagevs.Instantaneous(at an exact point)(over an interval of time)Limits and ContinuityLimits: a number that your function approaches, but does not necessarily get there.lim f(x) =f(1) = lim f(x) =lim f(x) =x 1x 1x 1f(1) = f(1) = Limits and ContinuityProperties and Limits: if lim f(x) = L and lim g(x) = M, thenSum

Difference

Product

Constant Multiple

Quotient

Powerlim (f(x) + g(x)) = L + M

lim (f(x) - g(x)) = L - M

lim (f(x) g(x)) = L M

lim [K f(x)] = K L

lim ( ) = (M 0)

lim [f(x)] = Lx cx cx cf(x)g(x)LMrsrsx cx cx cx cx cLimits and ContinuityOne- and Two- Sided Limits:lim f(x) =

lim f(x) =

lim f(x) =x c+x c-x cYou can find limits by substitution, graphs, or analysis.I put a spell on you you will like math class