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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 40E
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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.
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