(a) Express 3x- 32' + 20 +2 – 1 (* - 1)(2² +1) as a sum of rational functions of the form A, and B,r +C, (a,r + b,)" where A, B,, C3, a;, bi, c d, and e, are appropriate real numbers. Note: Factorise the rational function first. Do not calculate the constants Ai, B; and
(a) Express 3x- 32' + 20 +2 – 1 (* - 1)(2² +1) as a sum of rational functions of the form A, and B,r +C, (a,r + b,)" where A, B,, C3, a;, bi, c d, and e, are appropriate real numbers. Note: Factorise the rational function first. Do not calculate the constants Ai, B; and
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![te: Factorise the rational function first. Do mot calculate the constants Ai, Bj
3. (a) Express
3x - 32 + 20² +2 – 1
(*- 1)(22 + 1)
as a sum of rational functions of the form
A,
(a,a + b,)
B,» + C,
and
(c,a² +d;r + e;)"
where A, B, C, a;, bi, cj d; and e, are appropriate real numbers.
Note: Factorise the rational function first. Do not calculate the constants Ai,
and
(b) Let
2x
5x+9
(* – 1)(r+ 1).
Evaluate the
indefinite integralS(r)dr.
Hint: Do long division first.
(c) Use
evaluate
2.
dr.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23c82962-fdd3-4aae-a199-ce5241f64aad%2Ff1c244e5-467b-4c5b-8847-ea205118edb6%2Fb2cv57n7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:te: Factorise the rational function first. Do mot calculate the constants Ai, Bj
3. (a) Express
3x - 32 + 20² +2 – 1
(*- 1)(22 + 1)
as a sum of rational functions of the form
A,
(a,a + b,)
B,» + C,
and
(c,a² +d;r + e;)"
where A, B, C, a;, bi, cj d; and e, are appropriate real numbers.
Note: Factorise the rational function first. Do not calculate the constants Ai,
and
(b) Let
2x
5x+9
(* – 1)(r+ 1).
Evaluate the
indefinite integralS(r)dr.
Hint: Do long division first.
(c) Use
evaluate
2.
dr.
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