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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Presentation transcript:

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 trig. One of the uses of limits is to test for continuity.

Limits and Continuity Rates of Change and Limits: Averagevs.Instantaneous (at an exact point)(over an interval of time)

Limits and Continuity Limits: a number that your function approaches, but does not necessarily get there. lim f(x) = f(1) = lim f(x) = x  1 f(1) =

Limits and Continuity Properties and Limits: if lim f(x) = L and lim g(x) = M, then… Sum Difference Product Constant Multiple Quotient Power lim (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)] = L x  c f(x) g(x) LMLM rsrs rsrs x  c

Limits and Continuity One- and Two- Sided Limits: lim f(x) = x  c + x  c - x  c You can find limits by substitution, graphs, or analysis.

I put a spell on you… … you will like math class