Let fx) = 4 + 4x.Sketch the curve and the approximating rectangles for(a) Estimate the area under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints.202아20R =15151513Improve your estimate by using six rectangles.101010Sketch the curve and the approximating rectangies for R2아20o-12"O o-1-0.52 0 0-1 -0.52 0 0-1-0.50.50.5150.5 115-050.51.513131315(c) Repeat part (a) using a midpoints10M. -0Sketch the curve and the approximating rectangles for M2015151515o-1O 0-10 0-1O 0-1Sketch the curve and the approximating rectangles for Ro-1O -1O o-1O o-12아20-2아Sketch the curve and the approximating rectangles for M151315152아10101아1015131315101010100 0-10.5O 0-11o-1-0.50.515-0.50.5150 0-1-0.5-0.50.515(b) Repeat part (a) using a left enapoints.o-1O 0-1O o-10.5 1O o-1-a.50.51.5-05115-a.51.5-a.s0.51.5Sketch the curve and the approximating rectangies for(4) From your skatches in parts (a)-(c), which estimate appears to be the most accurate?2아OR1515-1310O 0-10 0-10-1

As you have asked more than three subparts, i am answering first three subparts only as…

Let fx) = 4 + x. (a) Estimate the ares under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints. R, Improve your estimate by using six rectangles. Sch the oune and he aporoumating rectangies for O o- O o- Sth the unve and the onating ectongies tor 13 o- -as 03 I 13 o- 13 0 o-1 13 O o-1 13 epet pet nganpores ne n enes 0-1 10-1

Let fx) = 4 + x. (a) Estimate the ares under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints. R, Improve your estimate by using six rectangles. Sch the oune and he aporoumating rectangies for O o- O o- Sth the unve and the onating ectongies tor 13 o- -as 03 I 13 o- 13 0 o-1 13 O o-1 13 epet pet nganpores ne n enes 0-1 10-1

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

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

Let fx) = 4 + 4x.
Sketch the curve and the approximating rectangles for
(a) Estimate the area under the graph of f, the x-axis, and the lines x = -1 and x = 2 using three rectangles and a right endpoints.
20
2아
20
R =
15
15
15
13
Improve your estimate by using six rectangles.
10
10
10
Sketch the curve and the approximating rectangies for R
2아
20
o-1
2"O o-1
-0.5
2 0 0-1 -0.5
2 0 0-1
-0.5
0.5
0.5
15
0.5 1
15
-05
0.5
1.5
13
13
13
15
(c) Repeat part (a) using a midpoints
10
M. -0
Sketch the curve and the approximating rectangles for M
20
15
15
15
15
o-1
O 0-1
0 0-1
O 0-1
Sketch the curve and the approximating rectangles for R
o-1
O -1
O o-1
O o-1
2아
20-
2아
Sketch the curve and the approximating rectangles for M
15
13
15
15
2아
10
10
1아
10
15
13
13
15
10
10
10
10
0 0-1
0.5
O 0-1
1
o-1
-0.5
0.5
15
-0.5
0.5
15
0 0-1
-0.5
-0.5
0.5
15
(b) Repeat part (a) using a left enapoints.
o-1
O 0-1
O o-1
0.5 1
O o-1
-a.5
0.5
1.5
-05
1
15
-a.5
1.5
-a.s
0.5
1.5
Sketch the curve and the approximating rectangies for
(4) From your skatches in parts (a)-(c), which estimate appears to be the most accurate?
2아
OR
15
15-
13
10
O 0-1
0 0-1
0-1

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