6. Evaluate fozdz, where C is the circle [2] = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. Hint: Let C: z(t) = 4 cost+i4 sint for 0≤t≤2. (Ans: 0) 7. Evaluate √ Edz, where C is the circle |2] = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. (Ans: 32mi) 8. Evaluate fc(z+1)dz, where C is given by z(t) = cost+i sint for 0 1), show that z²(z+1)' (a) IRR and HENCE that (b) lim IR = 0. R-00 21. If IR= 2-5 CR e²(+4) that lim IR = 0. R-00 dz, where CR is the semicircle below, centre 0, radius R > 2. Show
6. Evaluate fozdz, where C is the circle [2] = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. Hint: Let C: z(t) = 4 cost+i4 sint for 0≤t≤2. (Ans: 0) 7. Evaluate √ Edz, where C is the circle |2] = 4 taken with counter-clockwise (i.e. anti- clockwise) orientation. (Ans: 32mi) 8. Evaluate fc(z+1)dz, where C is given by z(t) = cost+i sint for 0 1), show that z²(z+1)' (a) IRR and HENCE that (b) lim IR = 0. R-00 21. If IR= 2-5 CR e²(+4) that lim IR = 0. R-00 dz, where CR is the semicircle below, centre 0, radius R > 2. Show
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
![6. Evaluate fozdz, where C is the circle [2] = 4 taken with counter-clockwise (i.e. anti-
clockwise) orientation.
Hint: Let C: z(t) = 4 cost+i4 sint for 0≤t≤2.
(Ans: 0)
7. Evaluate √ Edz, where C is the circle |2] = 4 taken with counter-clockwise (i.e. anti-
clockwise) orientation.
(Ans: 32mi)
8. Evaluate fc(z+1)dz, where C is given by z(t) = cost+i sint for 0<t</2.
i-2)
(Ans:
10. Evaluate √2dz, where C is the line segment from 1 to 1+i and z(t) = 1 + it for
0≤t≤1.
(Ans: -1+21/3)
14. Evaluate
(1/2)dz, where C is the circle || = 2 taken with clockwise orientation.
Hint: C: 2(t)=2 cost-i2 sint for 0≤t≤2.
15. Evaluate
0)
(Ans: -2πi)
(1/2)dz, where C is the circle || = 2 taken with clockwise orientation. (Ans:
20. If IR=
=fon
dz
where CR is the circle |2|= R (R> 1), show that
z²(z+1)'
(a) IRR and HENCE that
(b) lim IR = 0.
R-00
21. If IR=
2-5
CR e²(+4)
that lim IR = 0.
R-00
dz, where CR is the semicircle below, centre 0, radius R > 2. Show](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F155158b7-b900-47c4-a397-fbe9c98c96ca%2Fd6e4894a-8a38-419c-9a00-b56b18124915%2Fx1uinj_processed.png&w=3840&q=75)
Transcribed Image Text:6. Evaluate fozdz, where C is the circle [2] = 4 taken with counter-clockwise (i.e. anti-
clockwise) orientation.
Hint: Let C: z(t) = 4 cost+i4 sint for 0≤t≤2.
(Ans: 0)
7. Evaluate √ Edz, where C is the circle |2] = 4 taken with counter-clockwise (i.e. anti-
clockwise) orientation.
(Ans: 32mi)
8. Evaluate fc(z+1)dz, where C is given by z(t) = cost+i sint for 0<t</2.
i-2)
(Ans:
10. Evaluate √2dz, where C is the line segment from 1 to 1+i and z(t) = 1 + it for
0≤t≤1.
(Ans: -1+21/3)
14. Evaluate
(1/2)dz, where C is the circle || = 2 taken with clockwise orientation.
Hint: C: 2(t)=2 cost-i2 sint for 0≤t≤2.
15. Evaluate
0)
(Ans: -2πi)
(1/2)dz, where C is the circle || = 2 taken with clockwise orientation. (Ans:
20. If IR=
=fon
dz
where CR is the circle |2|= R (R> 1), show that
z²(z+1)'
(a) IRR and HENCE that
(b) lim IR = 0.
R-00
21. If IR=
2-5
CR e²(+4)
that lim IR = 0.
R-00
dz, where CR is the semicircle below, centre 0, radius R > 2. Show
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
