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4. The goal of this problem is to show that x² Q(x) = 1+x + is the quadratic approximation to f(x) = e" at the point a = : 0. (a) Consider the general form of a quadratic, namely Q(x) = bx² + cx + d where b, c, d are constants. Compute Q'(x) and Q"(x). (b) Solve the system of equations Q(0) = f(0) and Q'(0) = f'(0) and Q"(0) = f"(0) for b, c, d. Deduce that Q(x) = 1+ x + as claimed.

4. The goal of this problem is to show that x² Q(x) = 1+x + is the quadratic approximation to f(x) = e" at the point a = : 0. (a) Consider the general form of a quadratic, namely Q(x) = bx² + cx + d where b, c, d are constants. Compute Q'(x) and Q"(x). (b) Solve the system of equations Q(0) = f(0) and Q'(0) = f'(0) and Q"(0) = f"(0) for b, c, d. Deduce that Q(x) = 1+ x + as claimed.

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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The goal of this problem is to show that

is the quadratic approximation to f(x) = ex at the point a = 0.


a). Consider the general form of a quadratic, namely Q(x) = bx2 + cx + d where b, c, d are constants. Compute Q′(x) and Q′′(x).


b). Solve the system of equations Q(0) = f(0) and Q′(0) = f′(0) and Q′′(0) = f′′(0) for b, c, d.Deduce that ... as claimed.

The goal of this problem is to show that 4. x2 Q(x) = 1+ x + 2 is the quadratic approximation to f(x) = e® at the point a = 0. (a) Consider the general form of a quadratic, namely Q(x) constants. Compute Q'(x) and Q"(x). = bx2 + cx + d_where b, c, d are (b) Solve the system of equations Q(0) = f(0) and Q'(0) = f'(0) and Q"(0) = f"(0) for b, c, d. Deduce that x² Q(x) = 1+x + 2 as claimed.
Transcribed Image Text:The goal of this problem is to show that 4. x2 Q(x) = 1+ x + 2 is the quadratic approximation to f(x) = e® at the point a = 0. (a) Consider the general form of a quadratic, namely Q(x) constants. Compute Q'(x) and Q"(x). = bx2 + cx + d_where b, c, d are (b) Solve the system of equations Q(0) = f(0) and Q'(0) = f'(0) and Q"(0) = f"(0) for b, c, d. Deduce that x² Q(x) = 1+x + 2 as claimed.
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