In this problem we will first find an estimate to 1.5 using a Taylor polynomial P2(1.5) and then use the Remainder Estimation Theorem to approximate 1.5 - P2(1.5). This problem has parts (a)-(g). (a) What should f(x) and the center a be in order to compute a Taylor polynomial P,(x) at x= a? The function is f(x) = and the center is a = (b) Find the Taylor polynomial of order 2, i.e., P,(x), generated by the f(x) is part (a) at the center x= a from part (a). P2(x) = (c) Use P2(x) from part (b) to find an approximation to V1.5. (Your answer can be written as a sum of fractions.) 1.5 = (d) Compute f (3)(x) and f (4) (x). f(3) (x) =| and f(4(x) = (e) Which of the following is true? O A. f(t) < 0 and f (4) (t) < 0 for asts 1.5, so f ((x) is a negative, decreasing function on the interval [a, 1.5). O B. f(3) (t) > 0 and f (4) (t) < 0 for asts1.5, so f ((x) is a positive, decreasing function on the interval [a, 1.5]. O C. f(3) (t) > 0 and f(4) (t) > 0 for asts1.5, so f ((x) is a positive, increasing function on the interval [a, 1.5]. O D. f(3) (t) < 0 and f(4) (t) > 0 for asts 1.5, so f (3(x) is a negative, increasing function on the interval [a, 1.5). (f) Find smallest number M>0 that satisfies f (t) sM for all asts 1.5. M = since f(3) (t) will have an absolute maximum at t= in the interval [a, 1.5). (g) Fill in the blank. Using the value for M from part (f), the Remainder Estimation Theorem says that |1.5 - P,(1.5)| |R,(1.5)| 0.
In this problem we will first find an estimate to 1.5 using a Taylor polynomial P2(1.5) and then use the Remainder Estimation Theorem to approximate 1.5 - P2(1.5). This problem has parts (a)-(g). (a) What should f(x) and the center a be in order to compute a Taylor polynomial P,(x) at x= a? The function is f(x) = and the center is a = (b) Find the Taylor polynomial of order 2, i.e., P,(x), generated by the f(x) is part (a) at the center x= a from part (a). P2(x) = (c) Use P2(x) from part (b) to find an approximation to V1.5. (Your answer can be written as a sum of fractions.) 1.5 = (d) Compute f (3)(x) and f (4) (x). f(3) (x) =| and f(4(x) = (e) Which of the following is true? O A. f(t) < 0 and f (4) (t) < 0 for asts 1.5, so f ((x) is a negative, decreasing function on the interval [a, 1.5). O B. f(3) (t) > 0 and f (4) (t) < 0 for asts1.5, so f ((x) is a positive, decreasing function on the interval [a, 1.5]. O C. f(3) (t) > 0 and f(4) (t) > 0 for asts1.5, so f ((x) is a positive, increasing function on the interval [a, 1.5]. O D. f(3) (t) < 0 and f(4) (t) > 0 for asts 1.5, so f (3(x) is a negative, increasing function on the interval [a, 1.5). (f) Find smallest number M>0 that satisfies f (t) sM for all asts 1.5. M = since f(3) (t) will have an absolute maximum at t= in the interval [a, 1.5). (g) Fill in the blank. Using the value for M from part (f), the Remainder Estimation Theorem says that |1.5 - P,(1.5)| |R,(1.5)| 0.
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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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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![In this problem we will first find an estimate to V1.5 using a Taylor polynomial P2(1.5) and then use the Remainder Estimation Theorem to approximate V1.5 - P2(1.5). This problem has parts (a)-(g).
(a) What should f(x) and the center a be in order to compute a Taylor polynomial P,(x) at x = a?
The function is f(x) =
and the center is a =
(b) Find the Taylor polynomial of order 2, i.e., P2(x), generated by the f(x) is part (a) at the center x= a from part (a).
P2(x) =
(c) Use P,(x) from part (b) to find an approximation to V1.5. (Your answer can be written as a sum of fractions.)
1.5 =
(d) Compute f (3)(x) and f (4) (x).
f(3) (x) =|
and f4(x) =
(e) Which of the following is true?
O A. f8t) <0 and f(4 (t) < 0 for asts1.5, so f ((x) is a negative, decreasing function on the interval [a, 1.5].
O B. f(3) (t) > 0 and f (4) (t) < 0 for asts1.5, so f ((x) is a positive, decreasing function on the interval [a, 1.5].
O C. f(3) (t) > 0 and f (4) (t) > 0 for asts1.5, so f ((x) is a positive, increasing function on the interval [a, 1.5].
O D. f(3) (t) < 0 and f(4) (t) > 0 for asts 1.5, so f (3(x) is a negative, increasing function on the interval [a, 1.5).
(f) Find smallest number M>0 that satisfies f (t) sM for all asts 1.5.
M =
since f(3 (t) will have an absolute maximum at t =
in the interval [a, 1.5).
(g) Fill in the blank. Using the value for M from part (f), the Remainder Estimation Theorem says that
|1.5 - P,(1.5)| |R,(1.5)| 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfe7020d-97c0-4249-91b2-dc2ab2f45bf9%2Fce5ca692-ddd7-4dfa-a19d-120286130dcd%2Fehnisfg_processed.png&w=3840&q=75)
Transcribed Image Text:In this problem we will first find an estimate to V1.5 using a Taylor polynomial P2(1.5) and then use the Remainder Estimation Theorem to approximate V1.5 - P2(1.5). This problem has parts (a)-(g).
(a) What should f(x) and the center a be in order to compute a Taylor polynomial P,(x) at x = a?
The function is f(x) =
and the center is a =
(b) Find the Taylor polynomial of order 2, i.e., P2(x), generated by the f(x) is part (a) at the center x= a from part (a).
P2(x) =
(c) Use P,(x) from part (b) to find an approximation to V1.5. (Your answer can be written as a sum of fractions.)
1.5 =
(d) Compute f (3)(x) and f (4) (x).
f(3) (x) =|
and f4(x) =
(e) Which of the following is true?
O A. f8t) <0 and f(4 (t) < 0 for asts1.5, so f ((x) is a negative, decreasing function on the interval [a, 1.5].
O B. f(3) (t) > 0 and f (4) (t) < 0 for asts1.5, so f ((x) is a positive, decreasing function on the interval [a, 1.5].
O C. f(3) (t) > 0 and f (4) (t) > 0 for asts1.5, so f ((x) is a positive, increasing function on the interval [a, 1.5].
O D. f(3) (t) < 0 and f(4) (t) > 0 for asts 1.5, so f (3(x) is a negative, increasing function on the interval [a, 1.5).
(f) Find smallest number M>0 that satisfies f (t) sM for all asts 1.5.
M =
since f(3 (t) will have an absolute maximum at t =
in the interval [a, 1.5).
(g) Fill in the blank. Using the value for M from part (f), the Remainder Estimation Theorem says that
|1.5 - P,(1.5)| |R,(1.5)| 0.
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