Explanation ( s − r ) is a non repeated linear factor of Q ( s ) . So, Q ( s ) = ( s − r ) R ( s ) Here, R ( s ) ≠ 0 By partial fractions, P ( s ) Q ( s ) = A s − r + B R ( s ) P ( s ) Q ( s ) = A R ( s ) + B ( s − r ) ( s − r ) R ( s ) P ( s ) = A R ( s ) + B ( s − r ) ( 1 ) Substitute r for s in equation ( 1 ) .

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ISBN: 9780135902738

Author: Nagle

Publisher: PEARSON

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The relation between two quantities which displays how much greater one quantity is than another is called ratio.

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Chapter 7.4, Problem 38E

To determine

To prove:

The portion of the partial fraction expansion of P(s)/Q(s) corresponding to s−r is As−r

Where A is given by the formula

A=lims→r(s−r)P(s)Q(s)=P(r)Q(r).

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Chapter 7.4, Problem 37E

Chapter 7.4, Problem 39E

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Chapter 7 Solutions

MYLAB MATH-W/ETEXT F/FUND.DIFF.EQUAT.

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To prove: The portion of the partial fraction expansion of P ( s ) / Q ( s ) corresponding to s − r is A s − r Where A is given by the formula A = lim s → r ( s − r ) P ( s ) Q ( s ) = P ( r ) Q ( r ) .

Solution Summary: The author explains that (s) is a non-repeated linear factor of Q

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To prove:

The portion of the partial fraction expansion of P(s)/Q(s) corresponding to s−r is As−r

Where A is given by the formula

A=lims→r(s−r)P(s)Q(s)=P(r)Q(r).

Want to see the full answer?

Chapter 7 Solutions

To prove: The portion of the partial fraction expansion of P ( s ) / Q ( s ) corresponding to s − r is A s − r Where A is given by the formula A = lim s → r ( s − r ) P ( s ) Q ( s ) = P ( r ) Q ( r ) .

Solution Summary: The author explains that (s) is a non-repeated linear factor of Q

Concept explainers

Videos

To prove: The portion of the partial fraction expansion of P(s)/Q(s) corresponding to s−r is As−r Where A is given by the formula A=lims→r(s−r)P(s)Q(s)=P(r)Q(r).

Want to see the full answer?

Chapter 7 Solutions

To prove:

The portion of the partial fraction expansion of P(s)/Q(s) corresponding to s−r is As−r

Where A is given by the formula

A=lims→r(s−r)P(s)Q(s)=P(r)Q(r).