Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
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Chapter B, Problem 9P
To determine
The partial fraction decomposition of the given rational function.
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Is the following statement correct? Justify your answer. For the rational expression x/(x+1)(x-2)^2, the partial fraction decomposition is of the form A/x+1 + Bx+C/(x-2)^2
Solve problem as well.
Need help with both problems. The first problem deals with partial fraction decomposition, then need to be evaluated. The second problem details the direcrions
is the following statement correct? Justify your answer and complete solving the problem For the rational expression x/((x + 1) * (x - 2) ^ 2) the partial fraction decomposition is of the form d/(x + 1) + (Bx + C)/((x - 2) ^ 2)
Chapter B Solutions
Differential Equations and Linear Algebra (4th Edition)
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- Once you have a system of equations generated by the partial fraction decomposition, can you explain another method to solve it? For example if you had 7x+133x2+8x+15=Ax+1+B3x+5 , we eventually 7x+13=A(3x+5)+B(x+1) .Explain how you could intelligently choose an x-value that will eliminate either A or B and solve for A and B.arrow_forwardFor questions 9 and 10 we are doing partial fraction decomposition. On the answer key, for #9 we broke up (x^2-4) and (x^2-1) further using the difference of square formula. Why didn't we use this formula in number 10? And instead used Cx+D? How do I know how to differentiate between the methods?arrow_forwardPlease ssolve and show all steps. please explain why and how to use partial fraction decomposition on this type of problem ∫x /(x^3+8)dxarrow_forward
- Putting this into a partial fraction. Could the second fraction be (s-1)^2+1?arrow_forward(x4 + 1 )/(x5 +4x 3 ) Write out the form of the partial fraction decomposition ofthe function (as in Example 6). Do not determine the numericalvalues of the coefficients.arrow_forwardWhat is the form of the partial fraction decomposition of a rational function P ( x ) Q ( x ) if the degree of P is less than the degree of Q and has only distinct linear factors? What if a linear factor is repeated? What if Q(x) has an irreducible (non-factorable) quadratic factor (not repeated)? What if the quadratic factor is repeated?arrow_forward
- For integration of rational functions by partial fractions, how do you know what to choose as u for u-substitution, such as in problems 45 and 47, which are attached?arrow_forwardHello. Can you please show me how to solve this problem? Question: Find the partial fraction decomposition for the rational expression. 5x-3 / x(3x^2 + 1)^2 Thank you.arrow_forwardKindly please indicate complete solutions. Find the partial fraction decomposition of each rational expression.arrow_forward
- The form of the partial fraction decomposition of a rational fraction is given below. ((10x^2)+4x+24)/((x+1)(x^2+4)) = (A/(x+1))+((Bx+C)/((x^2)+4)) A=_______ B=___________ C=___________ Now evaluate the indefinite integral. ∫((10x^2)+4x+24)/((x+1)((x^2)+4))dx= _________________ +Carrow_forwardProblem 8 The form of the partial fraction decomposition for the integrand of ∫(8x+9)/((x^2)+6x+9)dx (upper limit=10, lower limit=3) is (A/denominator)+(B/denominator) Find the numbers A and B A=______________ B=________________arrow_forwardhow do I expand (x^2+1)/(x^2-7x+12) using partial fractions?arrow_forward
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