A First Course in Differential Equations with Modeling Applications (11th Edition)

Chapter 10

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120 ; The quantity can be written as . So it can ... more

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5040 ; The quantity can be written as . So it can... more

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; The quantity can be written as . So it can be ... more

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; The quantity can be written as . So it can be ... more

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; The quantity can be written as . So it can be ... more

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; The quantity can be written as . So it can be ... more

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; Substitute for in to obtain the quantity ... more

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; Substitute for in to obtain the quantity ... more

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; Substitute for in to obtain the quantity ... more

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; Substitute for in to obtain the quantity ... more

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; The quantity can be written as . So it can be ... more

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1.06863 ; The quantity can be written as . So it ... more

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; The quantity can be written as . So it can be ... more

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3.32325 ; The quantity can be written as . So it ... more

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; The quantity can be written as . So it can be ... more

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Let .Differentiate both sides of the equation ... more

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  ; The improper integral can be represented as .... more

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  ; The improper integral can be represented as .... more

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  ; The improper integral can be represented as .... more

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486 ; The improper integral can be represented as... more

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Consider the beta function .Substitute for and ... more

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Consider the beta function .Let .Differentiate the... more

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Consider the beta function .Let .Differentiate the... more

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; Let , and  Substitute 0 for and for and ... more

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; Let , and .Substitute for and for and ... more

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Let , and .Also, and can be represented as and... more

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Consider , and .Also, and can be represented as... more

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(21​−34​)(−25​)−(−1−2​63​)(−72​) Step-1Evaluate (... more

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Non singular;  ; Find the determinant of the ... more

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; Rewrite the system of equations in the form of... more

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; Rewrite the system of equations in the form of... more

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The third row of the reduced echelon form of a ... more

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The third and fourth row of the reduced echelon ... more

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; Find the determinant of the matrix .The ... more

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Eigenvalues: 0 and 3 Eigenvector: and ; ... more

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Eigenvalue: 4Eigenvector: ; Substitute for and ... more

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Eigenvalue: , , Eigenvector: , and ; Substitute... more

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Eigenvalues: 1, 2 and 3 Eigenvector: , , and ; ... more

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Eigenvalue: -2Eigenvector: and . ; Substitute ... more

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Eigenvalue: 1 and 3Eigenvector: , . ; Substitute... more

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Eigenvalue: 2, and Eigenvector: , and ; ... more

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Assume be a matrix of differentiable functions... more

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Substitute in the expression and apply  the ... more

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The matrix and are non singular therefore and .... more

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