Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables.(Round your answers to four decimal places. Percentages may be rounded to two decimal places. Use the rounded values for subsequent calculations.)У'%3D у, у(0) %3D 1; у(1.0)У(x) %3(explicit solution)h = 0.1XnYnActualAbsolute% Rel.ValueErrorError0.001.00001.00000.00000.000.101.10520.201.22140.301.34990.401.49180.501.64870.601.82210.702.01380.802.22550.902.45961.002.7183 h = 0.05XnYnActualAbsolute% Rel.ValueErrorError0.001.00001.00000.00000.000.051.05001.05130.00130.120.101.10251.10520.00270.240.151.15761.16180.00420.360.201.21551.22140.00590.480.251.27631.28400.00770.600.301.34011.34990.00980.730.351.40711.41910.01200.850.401.47751.49180.01430.960.451.55141.56830.01691.080.501.62901.64870.01971.190.551.71051.73330.02281.320.601.79601.82210.02611.430.651.88581.91550.02971.550.701.98012.01380.03371.670.752.07912.11700.03791.790.802.18312.22550.04241.910.852.29232.33960.04732.020.902.40692.45960.05272.140.952.52722.58570.05852.261.002.7183

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Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places. Use the rounded values for subsequent calculations.) y' = y, y(0) = 1; y(1.0) y(x) = (explicit solution) h = 0.1 Actual Value Absolute % Rel. Error Xn Yn Error 0.00 1.0000 1.0000 0.0000 0.00 0.10 1.1052 0.20 1.2214 0.30 1.3499 0.40 1.4918 0.50 1.6487 0.60 1.8221 0.70 2.0138 0.80 2.2255 0.90 2.4596 1.00 2.7183

Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places. Use the rounded values for subsequent calculations.) y' = y, y(0) = 1; y(1.0) y(x) = (explicit solution) h = 0.1 Actual Value Absolute % Rel. Error Xn Yn Error 0.00 1.0000 1.0000 0.0000 0.00 0.10 1.1052 0.20 1.2214 0.30 1.3499 0.40 1.4918 0.50 1.6487 0.60 1.8221 0.70 2.0138 0.80 2.2255 0.90 2.4596 1.00 2.7183

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter61: Areas Of Circles, Sectors, And Segments

Section: Chapter Questions

Problem 24A: A piece shown by the shaded portion is to be cut from a square plate 128 millimeters on a side. a....

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Question

Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables.
(Round your answers to four decimal places. Percentages may be rounded to two decimal places. Use the rounded values for subsequent calculations.)
У'%3D у, у(0) %3D 1; у(1.0)
У(x) %3
(explicit solution)
h = 0.1
Xn
Yn
Actual
Absolute
% Rel.
Value
Error
Error
0.00
1.0000
1.0000
0.0000
0.00
0.10
1.1052
0.20
1.2214
0.30
1.3499
0.40
1.4918
0.50
1.6487
0.60
1.8221
0.70
2.0138
0.80
2.2255
0.90
2.4596
1.00
2.7183

h = 0.05
Xn
Yn
Actual
Absolute
% Rel.
Value
Error
Error
0.00
1.0000
1.0000
0.0000
0.00
0.05
1.0500
1.0513
0.0013
0.12
0.10
1.1025
1.1052
0.0027
0.24
0.15
1.1576
1.1618
0.0042
0.36
0.20
1.2155
1.2214
0.0059
0.48
0.25
1.2763
1.2840
0.0077
0.60
0.30
1.3401
1.3499
0.0098
0.73
0.35
1.4071
1.4191
0.0120
0.85
0.40
1.4775
1.4918
0.0143
0.96
0.45
1.5514
1.5683
0.0169
1.08
0.50
1.6290
1.6487
0.0197
1.19
0.55
1.7105
1.7333
0.0228
1.32
0.60
1.7960
1.8221
0.0261
1.43
0.65
1.8858
1.9155
0.0297
1.55
0.70
1.9801
2.0138
0.0337
1.67
0.75
2.0791
2.1170
0.0379
1.79
0.80
2.1831
2.2255
0.0424
1.91
0.85
2.2923
2.3396
0.0473
2.02
0.90
2.4069
2.4596
0.0527
2.14
0.95
2.5272
2.5857
0.0585
2.26
1.00
2.7183

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