2. Caleulate the residues at the indicated poles coS 2 a)- z=0; il , 2 2 sin z (c) 따가, 1+22)22j. 2. Caleulate th...
ex4.13 Ex. 4.13. Calculate the residues at the poles indicated 1 COS 2 2 (a) 2 (b) sin 2 (c) 2 0; (1+z2)2
Problem #3: Find the residues of the following functions at z = 0 a) f(3) = 2* cos () b) f(3) = 1-cosa; c) f(3) = CS2 f(3) = 25(1 – 22) COS 2 COS 2 e) f(3) = 15e *e*1 f) f(3) = cosz - 1 9) f(3) = (sin 2)23 W f(z) = (eš – 1)2
Simplify the following trigonometric expression by following the indicated direction sin 0 1 + cos 0 Multiply 7- cos o by 1 + cos 0 sin e 1 + cos 0 1 - cos ' 1+ cos = *cos (Simplify your answer.)
pls help (6) Show that all singularities of f(2) and evaluate sin() are simple poles. Find the residues 22:-1 ffo where is the circle 2| = 3 in ced.
Establish the identity 1 - cos 0 sin 0 + sin 0 1 - cos 0 = 2 csc 0. Which of the following shows the key steps in establishing the identity? 1 - cos e sin 0 ОА. + sin e 1 cos e 1 - cos e B + sin e 1 - cos 0 sin e (1 - cos 0)2 + sine 2 = 2 csc 6 sin 0(1 - cos ) cOS (1 - cos 02...
15. Using that sin' (2) = cos(x), cos' (2) = - sin() show that arccot (0) = 1 +22
6. Use l'Hopital's rule to evaluate the following limits 1+cos (Te sin(z) (a) lim z-+0 log (-1) (b) lim 92I-2 cos(TI) (c) lim r sin Page 2 of 2 0 words
Find the flux integral SSs curl(Ē).d5, where F(x, y, z) = [2 cos(ny)+22 +22, 22 cos(z7/2) – sin(ny)e24, 222]T and S is the surface parametrized by F(s, t) = [(1 – 51/3) cos(t) – 4s, (1 – 51/3) sin(t), 5s]T with 0 <t< 27,0 < s < 1 and oriented so that the normal vectors point to the outside of the thorn.
in each case: (e) Compute y = sin(z)cos(r) for 0 < z < π/2
Rewrite-2 sin(x) + 1 cos (z) as A sin (z + φ) Preview A- Preview Note: φ should be in the interval-π < φ < π