Exact Accumulation and  AP Calculus. A). Sigma Notation REM: Ex.

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Presentation transcript:

Exact Accumulation and  AP Calculus

A). Sigma Notation REM: Ex.

Summation Formulas REM: Sum of the first 100 numbers ……

Finite Series EX 1. Evaluate using the formulas: EX 2. Evaluate using the formulas:

Infinite Series EX 3. Evaluate: REM: Limits at Infinity NOTICE: Inside: i is the variable. Outside: n is the variable EX 4. Evaluate:

AREA DEFN: The Area (accumulation) defined by a region in the plane is: We will use the RIGHT ENDPOINT and REGULAR PARTITIONS (easier!) THEOREM: The Limit ( as ) of the Under Approximation and the Over Approximation (and therefore any Riemann’s Sum) are equal.

a b a i th Rect. 1 st Rect. 2 nd Rect.

Area: Exact Accumulation Find the Area (accumulation) determined by the region bounded by and the x - axis on the interval [ 0, 2].

Area: Exact Accumulation Find the Area (accumulation) determined by the region bounded by and the x - axis on the interval [ 0, 3].

Area: Exact Accumulation Find the Area (accumulation) determined by the region bounded by and the x - axis on the interval [ 1, 2].

Area: Exact Accumulation Find the Area (accumulation) determined by the region bounded by and the x - axis on the interval [ 2, 4].

Last Update: 1/15/10 Assignment: Worksheet