Find the Taylor polynomial of order 2 for e* , centered about x, =1. A) e' (1–7(x-1)+49(;x–1)*) 49(x–1) B) e'|1-7(x – 1)+ 2 49(x – 1)² C) e'|1+7(x – 1)+ 2 D) e' (1-(x-1)+(x-1)*) E) e' (1+(x-1)-(x-1))
Find the Taylor polynomial of order 2 for e* , centered about x, =1. A) e' (1–7(x-1)+49(;x–1)*) 49(x–1) B) e'|1-7(x – 1)+ 2 49(x – 1)² C) e'|1+7(x – 1)+ 2 D) e' (1-(x-1)+(x-1)*) E) e' (1+(x-1)-(x-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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![The problem is to find the Taylor polynomial of order 2 for the function \( e^{7x} \), centered about \( x_0 = 1 \).
Options are as follows:
A) \( e^7 \left( 1 - 7(x-1) + 49(x-1)^2 \right) \)
B) \( e^7 \left[ 1 - 7(x-1) + \frac{49(x-1)^2}{2} \right] \)
C) \( e^7 \left[ 1 + 7(x-1) + \frac{49(x-1)^2}{2} \right] \)
D) \( e^7 \left( 1 - (x-1) + (x-1)^2 \right) \)
E) \( e^7 \left( 1 + (x-1) - (x-1)^2 \right) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F002560c4-f50e-4f4a-a33c-b3a98b864e70%2F06b26f6a-66ab-4caa-8e45-0d9af8c6e703%2Fsk660z_processed.png&w=3840&q=75)
Transcribed Image Text:The problem is to find the Taylor polynomial of order 2 for the function \( e^{7x} \), centered about \( x_0 = 1 \).
Options are as follows:
A) \( e^7 \left( 1 - 7(x-1) + 49(x-1)^2 \right) \)
B) \( e^7 \left[ 1 - 7(x-1) + \frac{49(x-1)^2}{2} \right] \)
C) \( e^7 \left[ 1 + 7(x-1) + \frac{49(x-1)^2}{2} \right] \)
D) \( e^7 \left( 1 - (x-1) + (x-1)^2 \right) \)
E) \( e^7 \left( 1 + (x-1) - (x-1)^2 \right) \)
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