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Unformatted text preview: c Kendra Kilmer March 1, 2012 Section 5.1 - Areas and Distances Example 1: Suppose a car travels at a constant 50 miles per hour for 2 hours. What is the total distance traveled? Example 2: Suppose a car travels 75 miles per hour for the ﬁrst hour, 70 miles per hour for the second hour, and
then 55 miles per hour for the last two hours of the trip. What is the total distance traveled? Example 3: A car starts moving at time t = 0 and gradually speeds up over time. Its velocity at a few particular
times is shown in the table below. Estimate how far the car travels during this 12 second period.
t (seconds) 0 4 8 12
v(t ) (ft/sec) 0 4 7 16 Example 4: An object travels with velocity v(t ) = t 2 where v is in feet per second and t is in seconds. Estimate how
far the object traveled during the ﬁrst three seconds, by using left endpoints and
a) three rectangles b) six rectangles 1 c Kendra Kilmer March 1, 2012 Example 5: Estimate the area under the graph of f (x) = x − 2 ln x on [1, 5]
a) using four approximating rectangles and right endpoints. b) using eight approximating rectangles and right endpoints. Deﬁnition: The area of the region that lies under the graph of the continuous and positive function f is the limit of
the sum of the areas of approximating rectangles: Section 5.1 Highly Suggested Homework Problems: 1, 3, 5, 11, 13, 15 2 ...
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This note was uploaded on 04/01/2012 for the course MATH 131 taught by Professor Allen during the Fall '08 term at Texas A&M.
- Fall '08