5.1 - Anonymous Student Assignment Section 5.1 due at...

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Anonymous Student Reynolds MAT 265 Spring 2013 Assignment Section 5.1 due 04/18/2013 at 11:59pm MST 1. (1 pt) Suppose f ( x ) = x 2 12 . (a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for f ( x ) on the interval 3 x 5. The value of this left endpoint Riemann sum is , and it is an ? the area of the region enclosed by y = f ( x ) , the x-axis, and the vertical lines x = 3 and x = 5. (b) The rectangles in the graph on the right illustrate a right endpoint Riemann sum for f ( x ) on the interval 3 x 5. The value of this right endpoint Riemann sum is , and it is an ? the area of the region enclosed by y = f ( x ) , the x-axis, and the vertical lines x = 3 and x = 5. Left endpoint Riemann sum Right endpoint Riemann sum SOLUTION: Solution: (A) The left endpoint Riemann sum is f ( 3 ) · 0 . 5 + f ( 3 . 5 ) · 0 . 5 + ··· + f ( 4 . 5 ) · 0 . 5 = ( 0 . 75 + 1 . 02083333333333 + ··· +) · 0 . 5 = 2 . 39583 . (B) The right endpoint Riemann sum is f ( 3 . 5 ) · 0 . 5 + f ( 4 ) · 0 . 5 + ··· + f ( 5 ) · 0 . 5 = ( 1 . 02083333333333 + 1 . 33333333333333 + ··· + 2 . 08333333333333 ) · 0 . 5 = 3 . 0625 . Correct Answers: 2.39583 underestimate of 3.0625 overestimate of 2. (1 pt) Suppose f ( x ) = 15 x . (a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for f ( x ) on the interval 4 x 6. The value of this left endpoint Riemann sum is , and it is an ? the area of the region enclosed by y = f ( x ) , the x-axis, and the vertical lines x = 4 and x = 6.
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  • Fall '13
  • Angles, Riemann sum, endpoint Riemann sum

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