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Suppose P4(x) (part 1 of 4) = 2-5x + 2x². - 4x³ + 5x¹ 2. f(0) = 3 3. f(0) 4. f(0) 5. f(0) = -2 = 4 = 2 (part 2 of 4) (ii) What is the value of f(³) (0)? 4 3 1. f(³) (0) 2. f(³) (0) 3. f(³) (0) 4. f(³) (0) 5. f(³) (0) = = 24 = -24 = -4 4 = 1/ 3 (part 3 of 4) (iii) Use p4 to estimate the value of f(0.1) 1. f(0.1) 1.7165 2. f(0.1) 1.4165 3. f(0.1) 1.5165 4. f(0.1) 1.8165 5. f(0.1) 1.6165

Suppose P4(x) (part 1 of 4) = 2-5x + 2x². - 4x³ + 5x¹ 2. f(0) = 3 3. f(0) 4. f(0) 5. f(0) = -2 = 4 = 2 (part 2 of 4) (ii) What is the value of f(³) (0)? 4 3 1. f(³) (0) 2. f(³) (0) 3. f(³) (0) 4. f(³) (0) 5. f(³) (0) = = 24 = -24 = -4 4 = 1/ 3 (part 3 of 4) (iii) Use p4 to estimate the value of f(0.1) 1. f(0.1) 1.7165 2. f(0.1) 1.4165 3. f(0.1) 1.5165 4. f(0.1) 1.8165 5. f(0.1) 1.6165

Calculus: Early Transcendentals
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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**Educational Content on Taylor Polynomials** In this exercise, we explore Taylor polynomials and their applications in estimating function values. **Given:** Suppose \( p_4(x) = 2 - 5x + 2x^2 - 4x^3 + 5x^4 \) is the degree 4 Taylor polynomial centered at \( x = 0 \) for some function \( f \). **Questions:** **(i) What is the value of \( f(0) \)?** 1. \( f(0) = -3 \) 2. \( f(0) = 3 \) 3. \( f(0) = -2 \) 4. \( f(0) = 4 \) 5. \( f(0) = 2 \) **(ii) What is the value of \( f^{(3)}(0) \)?** 1. \( f^{(3)}(0) = -\frac{4}{3} \) 2. \( f^{(3)}(0) = 24 \) 3. \( f^{(3)}(0) = -24 \) 4. \( f^{(3)}(0) = -4 \) 5. \( f^{(3)}(0) = \frac{4}{3} \) **(iii) Use \( p_4 \) to estimate the value of \( f(0.1) \).** 1. \( f(0.1) \approx 1.7165 \) 2. \( f(0.1) \approx 1.4165 \) 3. \( f(0.1) \approx 1.5165 \) 4. \( f(0.1) \approx 1.8165 \) 5. \( f(0.1) \approx 1.6165 \) By examining these polynomial coefficients, we delve into understanding the function's behavior near \( x = 0 \), how derivatives are represented in the polynomial, and how these can be used to estimate values such as \( f(0.1) \).
Transcribed Image Text:**Educational Content on Taylor Polynomials** In this exercise, we explore Taylor polynomials and their applications in estimating function values. **Given:** Suppose \( p_4(x) = 2 - 5x + 2x^2 - 4x^3 + 5x^4 \) is the degree 4 Taylor polynomial centered at \( x = 0 \) for some function \( f \). **Questions:** **(i) What is the value of \( f(0) \)?** 1. \( f(0) = -3 \) 2. \( f(0) = 3 \) 3. \( f(0) = -2 \) 4. \( f(0) = 4 \) 5. \( f(0) = 2 \) **(ii) What is the value of \( f^{(3)}(0) \)?** 1. \( f^{(3)}(0) = -\frac{4}{3} \) 2. \( f^{(3)}(0) = 24 \) 3. \( f^{(3)}(0) = -24 \) 4. \( f^{(3)}(0) = -4 \) 5. \( f^{(3)}(0) = \frac{4}{3} \) **(iii) Use \( p_4 \) to estimate the value of \( f(0.1) \).** 1. \( f(0.1) \approx 1.7165 \) 2. \( f(0.1) \approx 1.4165 \) 3. \( f(0.1) \approx 1.5165 \) 4. \( f(0.1) \approx 1.8165 \) 5. \( f(0.1) \approx 1.6165 \) By examining these polynomial coefficients, we delve into understanding the function's behavior near \( x = 0 \), how derivatives are represented in the polynomial, and how these can be used to estimate values such as \( f(0.1) \).
**Part 4 of 4** (iv) Use \( p_4 \) to estimate the value of \( f'(-0.1) \). 1. \( f'(-0.1) \approx -5.94 \) --- 2. \( f'(-0.1) \approx -5.84 \) 3. \( f'(-0.1) \approx -5.74 \) 4. \( f'(-0.1) \approx -5.64 \) 5. \( f'(-0.1) \approx -5.54 \)
Transcribed Image Text:**Part 4 of 4** (iv) Use \( p_4 \) to estimate the value of \( f'(-0.1) \). 1. \( f'(-0.1) \approx -5.94 \) --- 2. \( f'(-0.1) \approx -5.84 \) 3. \( f'(-0.1) \approx -5.74 \) 4. \( f'(-0.1) \approx -5.64 \) 5. \( f'(-0.1) \approx -5.54 \)
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