1. Solve the following problems using Euler's method with stepsizes of h = 0.2, 0.1, 0.05. Compute the error and relative error using the true answer Y(x). For selected values of x, observe the ratio by which the error decreases when h is halved. (a) Y'(x)= [cos(Y(x))]², Y(x) = tan¹(x) 0≤ x ≤ 10, Y(0) = 0; 1 (b) Y'(x)= 2[Y(x)]², 0≤ x ≤ 10, Y(0) = 0; 1+x² X Y(x) = 1+x²
1. Solve the following problems using Euler's method with stepsizes of h = 0.2, 0.1, 0.05. Compute the error and relative error using the true answer Y(x). For selected values of x, observe the ratio by which the error decreases when h is halved. (a) Y'(x)= [cos(Y(x))]², Y(x) = tan¹(x) 0≤ x ≤ 10, Y(0) = 0; 1 (b) Y'(x)= 2[Y(x)]², 0≤ x ≤ 10, Y(0) = 0; 1+x² X Y(x) = 1+x²
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 44E
Question
![1. Solve the following problems using Euler's method with stepsizes of h = 0.2, 0.1,
0.05. Compute the error and relative error using the true answer Y(x). For selected
values of x, observe the ratio by which the error decreases when h is halved.
(a) Y'(x)= [cos(Y(x))]²,
Y(x) = tan¹(x)
0≤ x ≤ 10,
Y(0) = 0;
1
(b) Y'(x)=
2[Y(x)]²,
0≤ x ≤ 10,
Y(0) = 0;
1+x²
X
Y(x) =
1+x²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98010ec1-9ca3-4b08-b004-c204532892b9%2Fe5a4b856-73b2-4872-83a4-a13578a47868%2Foyk53n_processed.png&w=3840&q=75)
Transcribed Image Text:1. Solve the following problems using Euler's method with stepsizes of h = 0.2, 0.1,
0.05. Compute the error and relative error using the true answer Y(x). For selected
values of x, observe the ratio by which the error decreases when h is halved.
(a) Y'(x)= [cos(Y(x))]²,
Y(x) = tan¹(x)
0≤ x ≤ 10,
Y(0) = 0;
1
(b) Y'(x)=
2[Y(x)]²,
0≤ x ≤ 10,
Y(0) = 0;
1+x²
X
Y(x) =
1+x²
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