a) Which of the following is the correct definition for the nth Taylor Polynomial for the function f (æ) at a = a? [ Select] "(a) Option I. Pn (a) = f (a) + ( - a) + (a - a)² + ( – a)*+....+ (n+1)! – a)" Option II. Pn (x) = f(x) + f' (x) (z- a) + ( - a)? + (- a) +....+( Option II. Pn. (x) = f (a) + f' (a) (x - a) + ( - a)? + (x - a)* +... + f" (a) fi (a) ( - a)" Option VI. P. (2) = f (a) + f (a) (x- a) + (- a') + (2 - a') +. f" (a) " (a) (2- a") b) Suppose now that f (x) is some differentiable function such that f (2) = 10 and that the nth derivative of f (x) at z = 2 is f(m) (2) = 2" for 1
a) Which of the following is the correct definition for the nth Taylor Polynomial for the function f (æ) at a = a? [ Select] "(a) Option I. Pn (a) = f (a) + ( - a) + (a - a)² + ( – a)*+....+ (n+1)! – a)" Option II. Pn (x) = f(x) + f' (x) (z- a) + ( - a)? + (- a) +....+( Option II. Pn. (x) = f (a) + f' (a) (x - a) + ( - a)? + (x - a)* +... + f" (a) fi (a) ( - a)" Option VI. P. (2) = f (a) + f (a) (x- a) + (- a') + (2 - a') +. f" (a) " (a) (2- a") b) Suppose now that f (x) is some differentiable function such that f (2) = 10 and that the nth derivative of f (x) at z = 2 is f(m) (2) = 2" for 1
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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![a) Which of the following is the correct definition for the nth Taylor Polynomial for the function f (x) at x = a?
[ Select ]
f" (a)
Option I. Pn (x) = f (a) +
(x – a) + ( – a)? +
a)°+.
(n+1)!
2 - a)"
Option II. Pn (2) = f (x) + f' (x) (x - a) + ( – a)² + ( – a)³ +..
(- a)"
Option III. P. (2) = f(a) + f' (a) (x - a) + ( – a)² + (x – a)³ +....+
(x- a)"
Option VI. Pn (a) = f (a) + f' (a) (x – a) + (2 – a') + (2 – a') +....+
(x – a")
b) Suppose now that f (x) is some differentiable function such that f (2) = 10 and that the nth derivative of f (x) at x = 2 is f(m) (2) = 2" for 1<n<5. Which of the following would be
the 5th Taylor Polynomial of f (x) at æ = 2? [ Select ]
Option 1. ps (2) %3D10 + (2-2) + 긁(2-2)2 1 곯(2-2), + 1(-2)* 1 금(22-2):
Option 2. ps (2) %3D10 + 2(z- 2) + 꽃 (z-2)2 + 좋(e-2)3 + 쮸(e-2)4 + 끓(2-2)°
Option 3. Ps (2) %3D2+ 2 (z - 2) + 흙(z-2)2 + 금(z-2)3 + 옮(2x-2)4 1 금(2-2)3
Option 4. Ps (2) %3D 10 + 2(x- 2) + 끓 (2-2), + 음 (2-2"), + 릎 (2-24)4 + 름(x-25)"](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb135572d-be3e-4d79-80b6-f74226b0d76c%2F43429069-5ce4-404c-be63-2c5c58d7a2b3%2Fewxqphb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Which of the following is the correct definition for the nth Taylor Polynomial for the function f (x) at x = a?
[ Select ]
f" (a)
Option I. Pn (x) = f (a) +
(x – a) + ( – a)? +
a)°+.
(n+1)!
2 - a)"
Option II. Pn (2) = f (x) + f' (x) (x - a) + ( – a)² + ( – a)³ +..
(- a)"
Option III. P. (2) = f(a) + f' (a) (x - a) + ( – a)² + (x – a)³ +....+
(x- a)"
Option VI. Pn (a) = f (a) + f' (a) (x – a) + (2 – a') + (2 – a') +....+
(x – a")
b) Suppose now that f (x) is some differentiable function such that f (2) = 10 and that the nth derivative of f (x) at x = 2 is f(m) (2) = 2" for 1<n<5. Which of the following would be
the 5th Taylor Polynomial of f (x) at æ = 2? [ Select ]
Option 1. ps (2) %3D10 + (2-2) + 긁(2-2)2 1 곯(2-2), + 1(-2)* 1 금(22-2):
Option 2. ps (2) %3D10 + 2(z- 2) + 꽃 (z-2)2 + 좋(e-2)3 + 쮸(e-2)4 + 끓(2-2)°
Option 3. Ps (2) %3D2+ 2 (z - 2) + 흙(z-2)2 + 금(z-2)3 + 옮(2x-2)4 1 금(2-2)3
Option 4. Ps (2) %3D 10 + 2(x- 2) + 끓 (2-2), + 음 (2-2"), + 릎 (2-24)4 + 름(x-25)"
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