1 / 12

Calculus Summation Methods for Area Accumulation Analysis

Learn about sum notation, finite series, infinite series, area accumulation using sigma notation and limits at infinity in calculus. Explore how to evaluate sums and areas with examples.

frey
Télécharger la présentation

Calculus Summation Methods for Area Accumulation Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Exact Accumulation and  AP Calculus

  2. A). Sigma Notation REM: Ex.

  3. REM: Sum of the first 100 numbers. 1+2+3+…….+98+99+100 Summation Formulas

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

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

  6. 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.

  7. 1st Rect. 2nd Rect. ith Rect. a b ith a

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

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

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

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

  12. Last Update: • 1/15/10 • Assignment: Worksheet

More Related