Explanation Given: The function is f ( x ) = 1 + x , a = 3 , Δ x = 0.2 . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where f ( a + Δ x ) = f ( a ) + f ′ ( a ) Δ x Percentage error = | Error Actual value | × 100 % Calculation: The function is f ( x ) = 1 + x , a = 3 , Δ x = 0.2 . We need to calculate Δ f ≈ f ′ ( a ) Δ x by using linear approximation of Δ f . Differentiate the function with respect to x f ′ ( x ) = 1 2 1 + x We apply the linear approximation to f ( x ) = 1 + x with a = 3 and Δ x = 0.2 . Use the formula: Δ f ≈ f ′ ( a ) Δ x Δ f ≈ f ′ ( a ) Δ x = 1 2 1 + 3 ( 0

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.1, Problem 9E

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Find the value of Δf. Also, compute both the errors and the percentage error.

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Chapter 4.1, Problem 8E

Chapter 4.1, Problem 10E

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A factorization A = PDP 1 is not unique. For A= 7 2 -4 1 1 1 5 0 2 1 one factorization is P = D= and P-1 30 = Use this information with D₁ = to find a matrix P₁ such that - -1 -2 0 3 1 - - 1 05 A-P,D,P P1 (Type an integer or simplified fraction for each matrix element.)

Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 30 -1 - 1 0 -1 400 0 0 1 A= 3 4 3 0 1 3 040 3 1 3 0 0 4 1 0 0 003 -1 0 -1 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A basis for the corresponding eigenspace is { A. There is one distinct eigenvalue, λ = B. In ascending order, the two distinct eigenvalues are λ₁ ... = and 2 = Bases for the corresponding eigenspaces are { and ( ), respectively. C. In ascending order, the three distinct eigenvalues are λ₁ = = 12/2 = and 3 = Bases for the corresponding eigenspaces are {}, }, and { respectively.

Chapter 4 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Find the value of Δ f . Also, compute both the errors and the percentage error.

Solution Summary: The author calculates the value of Delta f by using a linear approximation.

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