Suppose f(x)=x^2/12 (a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for f(x)f(x) on the interval 4≤x≤6 The value of this left endpoint Riemann sum is_, and it is an __ (over estimate of, equal to, under estimate of, there is ambuigity) the area of the region enclosed by y=f(x)y=f(x), the x-axis, and the vertical lines x=4x=4 and x=6x=6.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 3E

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Question

Suppose f(x)=x^2/12

(a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for f(x)f(x) on the interval 4≤x≤6 The value of this left endpoint Riemann sum is___________, and it is an ____________ (over estimate of, equal to, under estimate of, there is ambuigity) the area of the region enclosed by y=f(x)y=f(x), the x-axis, and the vertical lines x=4x=4 and x=6x=6.

(b) The rectangles in the graph on the right illustrate a right endpoint Riemann sum for f(x)f(x) on the interval 4≤x≤6 The value of this right endpoint Riemann sum is___________, and it is an_______________ (overestimate of, equal to, underestimate of, there is ambiguity) the area of the region enclosed by y=f(x)y=f(x), the x-axis, and the vertical lines x=4x=4 and x=6x=6.