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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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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 NOTICE: Inside: i is the variable. Outside: n is the variable EX 3. Evaluate: 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.
1st Rect. 2nd Rect. ith Rect. a b ith a
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]. Area: Exact Accumulation
Last Update: • 1/15/10 • Assignment: Worksheet