1 7. Define Taylor's Theorem and use it to find a second order approxima- tion to (1.1)¹/4. Suppre f(x) has a +1 devivatues at a het x be some other point. Taylo's Theorem saya: 2 • point. x=a. f(x) = f(a)+ f'(a)(x-a) + f "l(a)(x-²) + - + f(a)(x-²) + R₂ 2! n! To approximate of justure first 3 termand igne the rest. ntl R₁ = f(c)(x-a)" for some (n+1)! for some cin [a, x] or [24, α] depending xsa пна. Students may not see this so igine.
1 7. Define Taylor's Theorem and use it to find a second order approxima- tion to (1.1)¹/4. Suppre f(x) has a +1 devivatues at a het x be some other point. Taylo's Theorem saya: 2 • point. x=a. f(x) = f(a)+ f'(a)(x-a) + f "l(a)(x-²) + - + f(a)(x-²) + R₂ 2! n! To approximate of justure first 3 termand igne the rest. ntl R₁ = f(c)(x-a)" for some (n+1)! for some cin [a, x] or [24, α] depending xsa пна. Students may not see this so igine.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
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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can you please explain the answer by solving this question again?
![4
6
7. Define Taylor's Theorem and use it to find a second order approxima-
tion to (1.1)¹/4.
Suppre f(x) has
Let x be some other point.
Taylor's Theorem
ati derivatives at a point
2
says:
f(x) = f(a)+ f(a)(x-a) + f "(a)(x-1)³ + +5 () () + un
2!
R₁ = f" (c)(x-2)^" for some cin [a,x]
(n+1)!
on [22, a] depending
To approximate of just are
first 3 termand
guine the rest.
a=1
x-α = .1
2
f(1+1) = f(i) + fin (1) + f(n) (-1)³²
2.
~ 1+1(01) - 3 (00⁰1)
4
32
~ | +.025
≈ 1.02406
8
x=a.
03
32
True vole
They don't need to show the
100271
xsa
2 x 29.
Students may.
see this so
igine.
f(x) = x +
foll=1x²³¾/4
f"(x) == 3 x
16
f(1) = 1
f'al = 4
f" (1)
ast
= -3
16](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba7d748a-252c-474b-931e-93acb5db0c03%2Fb8b6f112-f22e-4518-ad75-cd7782cd1637%2F4zrwzl_processed.png&w=3840&q=75)
Transcribed Image Text:4
6
7. Define Taylor's Theorem and use it to find a second order approxima-
tion to (1.1)¹/4.
Suppre f(x) has
Let x be some other point.
Taylor's Theorem
ati derivatives at a point
2
says:
f(x) = f(a)+ f(a)(x-a) + f "(a)(x-1)³ + +5 () () + un
2!
R₁ = f" (c)(x-2)^" for some cin [a,x]
(n+1)!
on [22, a] depending
To approximate of just are
first 3 termand
guine the rest.
a=1
x-α = .1
2
f(1+1) = f(i) + fin (1) + f(n) (-1)³²
2.
~ 1+1(01) - 3 (00⁰1)
4
32
~ | +.025
≈ 1.02406
8
x=a.
03
32
True vole
They don't need to show the
100271
xsa
2 x 29.
Students may.
see this so
igine.
f(x) = x +
foll=1x²³¾/4
f"(x) == 3 x
16
f(1) = 1
f'al = 4
f" (1)
ast
= -3
16
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