The goal of this problem is to show thatis 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 that4.x2Q(x) = 1+ x +2is 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 thatx²Q(x) = 1+x +2as claimed.

Answered: Image /qna-images/answer/a90d620b-5350-43b2-90c1-28d53d96c489.jpg

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

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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