Find the Taylor polynomials of orders n = 0,1,2,3, and 4 about x = x, and then find the nth Taylor polynomials, Pn (x) for the function in sigma notation for f(x) = ax xo In2 Choose the correct answer. O po(x) = 1, P1(x) = 1 + a (x - In2), p2(x) = 1 + a(x - In2) + p3 (x)= 1+ a (x - In2) + p4(x)= 1+ a (x - In2) + Pn(x) = P3(x) = 29 Pn(x) = k=0 ○ po(x) = 29, p1(x) = 2ª[1 + a(x + In2)], p2(x) = 24 2ª|1. Pn(x) = P4(x) = 21+ a (x + In2) + 2º|1 P4(x) = 29 P3(x) = 2ª 1+ + ax + Pn(x) = ak(x - In2)k k! ○ po(x) = 29, P1(x) = 2ª[1 + ax], p2(x) = 24 p3(x)= a² k=0 P4(x)= a Pn(x) = 24ak(x + In2)k k! + a (x + In2) + 2² [1. 2ªkxk k! k=0 F P3(x) = 29 + ax + 2²|1. P4(x) = 29 a²(x-In2)² 21 k=0 a²(x - In2)² a³(x - In2)3 a(x - In2)4 21 3! 4! 2ª [1- ○ po(x) = a², P1(x) = a²[1 + a (x - In2)], p2(x) = ² : 2²1. 1+ a (x In2) + a²x2 + a (x - In2) + 29 [1- ak+x-In2)k k! + a(x In2) + + 24ak(x-In2) k! + + a (x - In2) + + O po(x) = 29, p1(x) = 2ª[1+ a (x - In2)], p2 (x) = 29 = 2ª|1 + a(x In2) + a²(x + In2)² 2! = 2ª [1 + ax + ²x²]. a³(x - In2)³ 31 a²(x - In2)² 2! a²(x - In2)² 2! a²(x + In2)² a³(x + In2)³ a¹(x + In2)4 2! 3! 4! + a (x + In2) + a³¹(x + In2)³ 35 a²(x - In2)² 2! a³(x-In2)³ 3! a²(x - In2)² a³(x - In2)³ a¹(x - In2)4 2! 3! + 4! 1+ a (x In2) + a²(x + ln2²]. 2! a³(x - In2)³ 3! - a²(x = 1n2)²]. 2! + - a²(x = ln2)²]. 2! a²(x - In2)² a³(x - In2)³ 4(x - In2)4 a¹(x = 1n2)4]. +
Find the Taylor polynomials of orders n = 0,1,2,3, and 4 about x = x, and then find the nth Taylor polynomials, Pn (x) for the function in sigma notation for f(x) = ax xo In2 Choose the correct answer. O po(x) = 1, P1(x) = 1 + a (x - In2), p2(x) = 1 + a(x - In2) + p3 (x)= 1+ a (x - In2) + p4(x)= 1+ a (x - In2) + Pn(x) = P3(x) = 29 Pn(x) = k=0 ○ po(x) = 29, p1(x) = 2ª[1 + a(x + In2)], p2(x) = 24 2ª|1. Pn(x) = P4(x) = 21+ a (x + In2) + 2º|1 P4(x) = 29 P3(x) = 2ª 1+ + ax + Pn(x) = ak(x - In2)k k! ○ po(x) = 29, P1(x) = 2ª[1 + ax], p2(x) = 24 p3(x)= a² k=0 P4(x)= a Pn(x) = 24ak(x + In2)k k! + a (x + In2) + 2² [1. 2ªkxk k! k=0 F P3(x) = 29 + ax + 2²|1. P4(x) = 29 a²(x-In2)² 21 k=0 a²(x - In2)² a³(x - In2)3 a(x - In2)4 21 3! 4! 2ª [1- ○ po(x) = a², P1(x) = a²[1 + a (x - In2)], p2(x) = ² : 2²1. 1+ a (x In2) + a²x2 + a (x - In2) + 29 [1- ak+x-In2)k k! + a(x In2) + + 24ak(x-In2) k! + + a (x - In2) + + O po(x) = 29, p1(x) = 2ª[1+ a (x - In2)], p2 (x) = 29 = 2ª|1 + a(x In2) + a²(x + In2)² 2! = 2ª [1 + ax + ²x²]. a³(x - In2)³ 31 a²(x - In2)² 2! a²(x - In2)² 2! a²(x + In2)² a³(x + In2)³ a¹(x + In2)4 2! 3! 4! + a (x + In2) + a³¹(x + In2)³ 35 a²(x - In2)² 2! a³(x-In2)³ 3! a²(x - In2)² a³(x - In2)³ a¹(x - In2)4 2! 3! + 4! 1+ a (x In2) + a²(x + ln2²]. 2! a³(x - In2)³ 3! - a²(x = 1n2)²]. 2! + - a²(x = ln2)²]. 2! a²(x - In2)² a³(x - In2)³ 4(x - In2)4 a¹(x = 1n2)4]. +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![Find the Taylor polynomials of orders n = 0,1,2,3, and 4 about x = xo, and then find the nth Taylor polynomials, Pn (x) for the
function in sigma notation for
f(x) = ax xo In2
Choose the correct answer.
O po(x) = 1,
P1(x) = 1 + a (x - In2), p2(x) = 1 + a(x - In2) +
P3(x) = 1+ a (x - In2) +
p4(x)= 1+ a (x - In2) +
Pn(x) =
P3(x) = 29
Pn(x) =
Ⓒ po(x) = 29,
p1(x) = 2ª [1 + a (x + In2)], p2(x) = 24
k=0
P3(x) =
2ª|1.
P4(x) = 21+ a (x + In2) +
201
Pn(x) =
P4(x) = 29
= 2ª [1-
ak(x - In2)k
k!
Pn(x) =
○ po(x) = 29,
P1(x) = 2ª[1 + ax], p2(x) = 24
p3(x)= a²
k=0
P4(x)= a
Pn(x) =
24ak(x + In2)k
k
+ a(x + In2) +
2² [1.
P3(x) = 29
2ªkxk
k!
k=0
F
+ ax +
p4(x) = 29
+ ax +
a²|1.
a²(x-In2)²
21
O po(x) = a²,
P1(x) = a²[1 + a(x - In2)], p2 (x)= a²
a²(x - In2)² a³(x - In2)³ a(x - In2)4
21
3!
4!
k=0
2ª|1-
a²x2
+ a(x - In2) +
20[1-
ak+x-In2)k
k!
+ a(x - In2) +
+
+
+ a (x - In2) +
2ªak (x-In2)k
a²(x + In2)²
2!
= 2ª [1 + ax + ²x²].
O po(x) = 29,
P1(x) = 2ª[1 + a(x - In2)], p2(x) = 2ª
29/11
+ a(x In2) +
a³(x - In2)³
31
a²(x - In2)²
2!
a²(x + In2)² a³(x + In2)³
2!
3!
a²(x - In2)²
2!
+ a (x + In2) +
a³(x +
P(x + In
In2)³
: 2²1. + a (x In2) +
a²(x - In2)²
2!
a³(x-In2)³
3!
a²(x - In2)² a³(x - In2)³ a¹(x - In2)4
+
2!
3!
4!
1+ a (x - In2) +
a²(x + In2)2
2!
a³(x - In2)³
3!
a²(x - In2)²
=
2!
a¹(x + In2)4
4!
+
-
a²(x = in2)²].
2!
a²(x - In2)² a³(x - In2)³ 4(x - In2)4
a¹(x = 1n2)4].
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5596b0d-bcdf-4f62-8113-fe2bcdce8faa%2Fa22f820f-5c93-4e17-ba07-cb79027a66c3%2Farrtzq5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the Taylor polynomials of orders n = 0,1,2,3, and 4 about x = xo, and then find the nth Taylor polynomials, Pn (x) for the
function in sigma notation for
f(x) = ax xo In2
Choose the correct answer.
O po(x) = 1,
P1(x) = 1 + a (x - In2), p2(x) = 1 + a(x - In2) +
P3(x) = 1+ a (x - In2) +
p4(x)= 1+ a (x - In2) +
Pn(x) =
P3(x) = 29
Pn(x) =
Ⓒ po(x) = 29,
p1(x) = 2ª [1 + a (x + In2)], p2(x) = 24
k=0
P3(x) =
2ª|1.
P4(x) = 21+ a (x + In2) +
201
Pn(x) =
P4(x) = 29
= 2ª [1-
ak(x - In2)k
k!
Pn(x) =
○ po(x) = 29,
P1(x) = 2ª[1 + ax], p2(x) = 24
p3(x)= a²
k=0
P4(x)= a
Pn(x) =
24ak(x + In2)k
k
+ a(x + In2) +
2² [1.
P3(x) = 29
2ªkxk
k!
k=0
F
+ ax +
p4(x) = 29
+ ax +
a²|1.
a²(x-In2)²
21
O po(x) = a²,
P1(x) = a²[1 + a(x - In2)], p2 (x)= a²
a²(x - In2)² a³(x - In2)³ a(x - In2)4
21
3!
4!
k=0
2ª|1-
a²x2
+ a(x - In2) +
20[1-
ak+x-In2)k
k!
+ a(x - In2) +
+
+
+ a (x - In2) +
2ªak (x-In2)k
a²(x + In2)²
2!
= 2ª [1 + ax + ²x²].
O po(x) = 29,
P1(x) = 2ª[1 + a(x - In2)], p2(x) = 2ª
29/11
+ a(x In2) +
a³(x - In2)³
31
a²(x - In2)²
2!
a²(x + In2)² a³(x + In2)³
2!
3!
a²(x - In2)²
2!
+ a (x + In2) +
a³(x +
P(x + In
In2)³
: 2²1. + a (x In2) +
a²(x - In2)²
2!
a³(x-In2)³
3!
a²(x - In2)² a³(x - In2)³ a¹(x - In2)4
+
2!
3!
4!
1+ a (x - In2) +
a²(x + In2)2
2!
a³(x - In2)³
3!
a²(x - In2)²
=
2!
a¹(x + In2)4
4!
+
-
a²(x = in2)²].
2!
a²(x - In2)² a³(x - In2)³ 4(x - In2)4
a¹(x = 1n2)4].
+
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