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Warm Up

Warm Up. Read the paragraph at the top of page 267 titled “Chapter 6 Overview” Then continue to read all of page 267. 6 .1 Estimating with Finite Sums. Goal: Calculate the distance traveled and use the RAM method. . Example.

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Warm Up

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  1. Warm Up Read the paragraph at the top of page 267 titled “Chapter 6 Overview” Then continue to read all of page 267

  2. 6.1 Estimating with Finite Sums • Goal: Calculate the distance traveled and use the RAM method.

  3. Example • Consider an object moving at a constant rate of 3 ft/sec. How far did it go after 4 sec? Since rate . time = distance: After 4 seconds, the object has gone 12 feet.

  4. Example velocity time If we draw a graph of the velocity, the distance that the object travels is equal to the area under the line.

  5. If the velocity is not constant, we might guess that the distance traveled is still equal to the area under the curve. We could estimate the area under the curve by drawing rectangles under the curve.

  6. Big Idea! Area under the velocity curve represents the total distance traveled by an object.

  7. Three different ways to draw rectangles Right-hand Rectangular Approximation Method . Left-hand Rectangular Approximation Method . Midpoint Rectangular Approximation Method .

  8. Example using LRAM Approximate area: A particle moves at a velocity of How far did the particle travel after 4 seconds.

  9. Approximate area: Same Example using RRAM 1 2 3 4

  10. Example of MRAM Very similar to the other two. See example #1 on page 268.

  11. Vocab Circumscribed rectangles are all above the curve: Inscribed rectangles are all below the curve:

  12. Example • A particle starts at x=0 and travels along the x axis with velocity v(t)=4. Where is the particle at t=7? • Answer: Find the area of the rectangle under the curve to see the particle is at x=28.

  13. Homework!

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