(i) import the numpy library and your favourite function plotting library (for example, matplotlib.pyplot). (ii) Either by using the def keyword or using a lambda function, define the following function: f(x) = = x³_ - 2x + 6 esin(z) In(x¹ + 3)* (iii) Plot the function f on the interval [-10, 10] and include the plot in your coursework submission. You may annotate the graph as much or as little as you like, but at a bare minimum you should label the x and y axes.
(i) import the numpy library and your favourite function plotting library (for example, matplotlib.pyplot). (ii) Either by using the def keyword or using a lambda function, define the following function: f(x) = = x³_ - 2x + 6 esin(z) In(x¹ + 3)* (iii) Plot the function f on the interval [-10, 10] and include the plot in your coursework submission. You may annotate the graph as much or as little as you like, but at a bare minimum you should label the x and y axes.
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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Question
![(a) In a single Python file and in the order described, do the following:
(i) import the numpy library and your favourite function plotting library (for example,
matplotlib.pyplot).
(ii) Either by using the def keyword or using a lambda function, define the following
function:
f(x) =
=
x³ - 2x +6
esin(x) In(x+3)
(iii) Plot the function f on the interval [—10, 10] and include the plot in your coursework
submission. You may annotate the graph as much or as little as you like, but at a
bare minimum you should label the x and y axes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e693cf-3870-4eab-9920-bd211e6a8ee6%2F6f2feb18-9965-4dc4-951a-01d7f0ab7a57%2Fjntqms_processed.png&w=3840&q=75)
Transcribed Image Text:(a) In a single Python file and in the order described, do the following:
(i) import the numpy library and your favourite function plotting library (for example,
matplotlib.pyplot).
(ii) Either by using the def keyword or using a lambda function, define the following
function:
f(x) =
=
x³ - 2x +6
esin(x) In(x+3)
(iii) Plot the function f on the interval [—10, 10] and include the plot in your coursework
submission. You may annotate the graph as much or as little as you like, but at a
bare minimum you should label the x and y axes.
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![(b) For the function f from part (a), could the Bisection method be used to find a root in the
interval [10, 10]? Say exactly why or why not. If it can be used, give two starting values
that you could use which would guarantee that the Bisection method would converge to
a root of f in [-10, 10].
(c) Let L be
1
Come up with a function
which has root at x = L and for which the Bisection method could be successfully used to
find L using x= 0 and x = L+2 as starting values. Next, calculate how many iterations
of the Bisection method with starting values 0 and L+2 would be required to guarantee
that the root L of f is approximated with an absolute error of 0.0001 or less (but also
assuming you do not know that L is the root).](https://content.bartleby.com/qna-images/question/38e693cf-3870-4eab-9920-bd211e6a8ee6/b38faec8-3a8a-4a49-990f-2772656cb244/xiuvwq_processed.png)
Transcribed Image Text:(b) For the function f from part (a), could the Bisection method be used to find a root in the
interval [10, 10]? Say exactly why or why not. If it can be used, give two starting values
that you could use which would guarantee that the Bisection method would converge to
a root of f in [-10, 10].
(c) Let L be
1
Come up with a function
which has root at x = L and for which the Bisection method could be successfully used to
find L using x= 0 and x = L+2 as starting values. Next, calculate how many iterations
of the Bisection method with starting values 0 and L+2 would be required to guarantee
that the root L of f is approximated with an absolute error of 0.0001 or less (but also
assuming you do not know that L is the root).
Solution
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