Suppose g is a function which has continuous derivatives, and that g(6) = 1, g′(6) = −3, g″(6) = −2, g′″ (6) = 2. (a) What is the Taylor polynomial of degree 2 for g near 6? P₂(x) = (b) What is the Taylor polynomial of degree 3 for g near 6? P3(x) = = (c) Use the two polynomials that you found in parts (a) and (b) to approximate g(6.1). With P2, g(6.1) ≈ With P3, 9(6.1) ≈
Suppose g is a function which has continuous derivatives, and that g(6) = 1, g′(6) = −3, g″(6) = −2, g′″ (6) = 2. (a) What is the Taylor polynomial of degree 2 for g near 6? P₂(x) = (b) What is the Taylor polynomial of degree 3 for g near 6? P3(x) = = (c) Use the two polynomials that you found in parts (a) and (b) to approximate g(6.1). With P2, g(6.1) ≈ With P3, 9(6.1) ≈
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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l10 and l11 solve both please
Transcribed Image Text:Suppose g is a function which has continuous derivatives, and that g(6) = 1, g′(6) = −3, g″(6) = −2, g′″ (6) = 2.
(a) What is the Taylor polynomial of degree 2 for g near 6?
P₂(x) =
(b) What is the Taylor polynomial of degree 3 for g near 6?
P3(x) =
=
(c) Use the two polynomials that you found in parts (a) and (b) to approximate g(6.1).
With P2, g(6.1) ≈
With P3, 9(6.1) ≈
Transcribed Image Text:Suppose that
Find each of the following:
d
±(r²e²²) |_
dz
• (2³e²²),
you are told that the Taylor series of f(x) = x³e²² about x = 0 is
drº
|z=0
=
x⁹
+ + +
x11
2! 3!
+
x 13
4!
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