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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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
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
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