(a) Graph both e and its linear approximation on the same plot, displaying a values in the interval [0, 2]. What is the exact value of e0.1 and its approximate value from your linear approximation? Compute the relative error. (b) Find a quadratic approximation to f(x) e near x = 0. Graph both e and its quadratic approximation on the same plot (using the same scale as be- fore). What is the approximate value of e0.1 from your quadratic approximation? Compute the relative error. =
(a) Graph both e and its linear approximation on the same plot, displaying a values in the interval [0, 2]. What is the exact value of e0.1 and its approximate value from your linear approximation? Compute the relative error. (b) Find a quadratic approximation to f(x) e near x = 0. Graph both e and its quadratic approximation on the same plot (using the same scale as be- fore). What is the approximate value of e0.1 from your quadratic approximation? Compute the relative error. =
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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![(a) Graph both et and its linear approximation on the same plot, displaying a values
in the interval [0, 2]. What is the exact value of e0.1 and its approximate value
from your linear approximation? Compute the relative error.
(b) Find a quadratic approximation to f(x) e near x = 0. Graph both e
and its quadratic approximation on the same plot (using the same scale as be-
fore). What is the approximate value of e0.1 from your quadratic approximation?
Compute the relative error.
=
(c) We can continue to add terms to our approximation. Find a formula for the
"cubic approximation" C(r) of a function g(x) around x = c. You should leave
your answer in terms of g and its derivatives.
(d) Repeat the previous two steps but for a cubic approximation using the formula
you found in the previous step. What is the approximate value of e0.1 using
your cubic approximation?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e51f0f4-140a-4430-91a7-57800eabe18a%2F498f4afd-1883-4289-b4dd-0462f8b64e3f%2Foptf8ci_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Graph both et and its linear approximation on the same plot, displaying a values
in the interval [0, 2]. What is the exact value of e0.1 and its approximate value
from your linear approximation? Compute the relative error.
(b) Find a quadratic approximation to f(x) e near x = 0. Graph both e
and its quadratic approximation on the same plot (using the same scale as be-
fore). What is the approximate value of e0.1 from your quadratic approximation?
Compute the relative error.
=
(c) We can continue to add terms to our approximation. Find a formula for the
"cubic approximation" C(r) of a function g(x) around x = c. You should leave
your answer in terms of g and its derivatives.
(d) Repeat the previous two steps but for a cubic approximation using the formula
you found in the previous step. What is the approximate value of e0.1 using
your cubic approximation?
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