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Exact Accumulation and . AP Calculus. A). Sigma Notation. REM:. Ex. REM: Sum of the first 100 numbers. 1+2+3+…….+98+99+100. Summation Formulas. Finite Series. EX 1. Evaluate using the formulas:. EX 2. Evaluate using the formulas:. Infinite Series. REM: Limits at Infinity.

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finite series
Finite Series

EX 1. Evaluate using the formulas:

EX 2. Evaluate using the formulas:

infinite series
Infinite Series

REM: Limits at Infinity

NOTICE: Inside: i is the variable.

Outside: n is the variable

EX 3. Evaluate:

EX 4. Evaluate:

slide6
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.

slide7

1st

Rect.

2nd

Rect.

ith

Rect.

a

b

ith

a

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
area exact accumulation1

Find the Area (accumulation) determined by the region bounded

by and the x - axis on the interval [ 0, 3].

Area: Exact Accumulation
area exact accumulation2

Find the Area (accumulation) determined by the region bounded

by and the x - axis on the interval [ 1, 2].

Area: Exact Accumulation
area exact accumulation3

Find the Area (accumulation) determined by the region bounded

by and the x - axis on the interval [ 2, 4].

Area: Exact Accumulation
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  • 1/15/10
  • Assignment: Worksheet