Find the Taylor polynomials of orders n = 0,1.2,3, and 4 about x = x9, and then find the nth Taylor polynomials, p.(x) for the function in sigma notation for fw) = e"; Xo = In7 Choose the correct answer. O po(x) = 7", Pi(x) = 7 [1 + a(x+ In7)], p2(x) = 7" | 1+ a(x + In7) + du+In7)*] 2!

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the Taylor polynomials of orders n 0,1,2,3, and 4 about x = xo, and then find the nth Taylor polynomials, p.(x) for the
function in sigma notation for
fw) = e: x = In7
Choose the correct answer.
O po(x) = 7",
Pi(x) = 7 [1+ a(x+ In7)]. p2(x) = 7" 1+ a(x + In7) +
Pa+ In7)*
2!
ax + In7), a'(x+ In7)
P3(x) = 7° 1+ a(x + In7) +
21
3!
P4(x) = 7° 1+ a(x+ In7) +
«+ In7) a'x + In7), ax + In7)
21
3!
4!
Pa(x) = 7"a*(x + In7
k!
k=0
O po(x) = 7",
P1(x) = 7°[1 + a(x- In7)], p2(x) = 7" | 1+ a(x – In7) +
a°& – In7)²
2!
P3(x) = 7° 1+ a(x- In7) +
a (x – In7)
ax – In7)
2!
3!
P4(x) = 7" 1+ a(x-In7) +
a (x – In7)²
a° (x – In7)
d(x - In7)*
2!
3!
4!
7 a (x-In7)*
Σ
Pn(x) =
k!
k=0
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, p.(x) for the function in sigma notation for fw) = e: x = In7 Choose the correct answer. O po(x) = 7", Pi(x) = 7 [1+ a(x+ In7)]. p2(x) = 7" 1+ a(x + In7) + Pa+ In7)* 2! ax + In7), a'(x+ In7) P3(x) = 7° 1+ a(x + In7) + 21 3! P4(x) = 7° 1+ a(x+ In7) + «+ In7) a'x + In7), ax + In7) 21 3! 4! Pa(x) = 7"a*(x + In7 k! k=0 O po(x) = 7", P1(x) = 7°[1 + a(x- In7)], p2(x) = 7" | 1+ a(x – In7) + a°& – In7)² 2! P3(x) = 7° 1+ a(x- In7) + a (x – In7) ax – In7) 2! 3! P4(x) = 7" 1+ a(x-In7) + a (x – In7)² a° (x – In7) d(x - In7)* 2! 3! 4! 7 a (x-In7)* Σ Pn(x) = k! k=0
O Po(x) = a',
P1(x) = a'[1 + a(x – In7)). p2(x) = a'
a (x- In7)
+ a(x – In7) +
2!
a² (x – In7) a (x – In7)
3!
P3(x) = a
+ a(x – In7) +
2!
a(x- In7) a (x – In7) a (x- In7)
4!
P4(x) = a' 1+ a(x – In7) +
%3D
2!
3!
ak+7 (x- In7)
Pa(x) =
k!
k=0
O po(x) = 1,
a (x- In7)
P1(x) = 1+ a(x- In7), p2(x) = 1+ a(x – In7) +
%3D
2!
a (x - In7) a (x – In7)
P3 (x) = 1+ a(x- In7) +
%3D
2!
3!
x- In7) a'(x – In7)
a x- In7)
P4(x) = 1 + a(x – In7) +
2!
3!
4!
a(x-In7y*
Σ
P.(x) =
k!
k-0
O po(x) = 7",
P1(X) =7"[1+ ax), p2(x) = 7“ 1+
P3(x) = 7"1+ ax +
+.
2!
3!
ax a'x
P4(x) = 7" I+ ax +
21
3!
7 ax
P.(x) =
k!
Transcribed Image Text:O Po(x) = a', P1(x) = a'[1 + a(x – In7)). p2(x) = a' a (x- In7) + a(x – In7) + 2! a² (x – In7) a (x – In7) 3! P3(x) = a + a(x – In7) + 2! a(x- In7) a (x – In7) a (x- In7) 4! P4(x) = a' 1+ a(x – In7) + %3D 2! 3! ak+7 (x- In7) Pa(x) = k! k=0 O po(x) = 1, a (x- In7) P1(x) = 1+ a(x- In7), p2(x) = 1+ a(x – In7) + %3D 2! a (x - In7) a (x – In7) P3 (x) = 1+ a(x- In7) + %3D 2! 3! x- In7) a'(x – In7) a x- In7) P4(x) = 1 + a(x – In7) + 2! 3! 4! a(x-In7y* Σ P.(x) = k! k-0 O po(x) = 7", P1(X) =7"[1+ ax), p2(x) = 7“ 1+ P3(x) = 7"1+ ax + +. 2! 3! ax a'x P4(x) = 7" I+ ax + 21 3! 7 ax P.(x) = k!
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