Example 2: Using four rectangles to estimate the area between the graph of the given function and the x-axis on the given interval. Construct three estimates for the function using: left endpoints, right endpoints and midpoints of the subinterval. For each estimate, give a sketch which includes the represented rectangles. f (x) = V4 – x² on [-2,2] a) Show work for using left-hand endpoints estimate.

Example 2: Using four rectangles to estimate the area between the graph of the given function and the x-axis on the given interval. Construct three estimates for the function using: left endpoints, right endpoints and midpoints of the subinterval. For each estimate, give a sketch which includes the represented rectangles. f (x) = V4 – x² on [-2,2] a) Show work for using left-hand endpoints estimate.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

Example 2: Using four rectangles to estimate the area between the graph of the given function
and the x-axis on the given interval. Construct three estimates for the function using: left
endpoints, right endpoints and midpoints of the subinterval. For each estimate, give a sketch
which includes the represented rectangles.
f(x) = v4 – x² on [-2,2]
a) Show work for using left-hand endpoints estimate.
3-
2
1
-3
-2
-1
2
-1
--2
-3

b) Show work for right hand endpoint estimate.
3
1-
-2
-1
3.
-1
-2
c) Show work for midpoint estimate.
3.
-2
13
1
2
3
-1
-2

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