2. Evaluate a. [sin z,d/dz] b. [d2/dx,ax2 + bx + c] where a, b, and c...
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) - (sin t, cos t, sin 2t), 0 s t s 27. (Hint: Observe that C lies on the surface z - 2xy.) F dr- 6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) -...
calculus 3 Tar LAami Jum er Z01J -z2 z sin x dy dz dx 1 8. Evaluate L Tar LAami Jum er Z01J -z2 z sin x dy dz dx 1 8. Evaluate L
What are the results of operating on the following functions with the operators d/dx and d2/dx2 : a) 4x-3 b) cos(bx), c) eikx d) (x2–i) ? What functions are eigenfunctions of these operators? What are the corresponding eigenvalues?
use residue theorem to evaluate the following integrals sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?
23 y?z? sin(x4) dx dy dz
Evaluate the integral. 2 2 3 SS Sy sin zdxdy dz 0 0 0 2 2x 3x SSS y sin z dx dy dz = 0 0 0 0 (Type an exact answer.)
1. Evaluate the complex integral: ∫C [zRe(z) − z¯Im(z)]dz, where C is the line segment joining −1 to i. (z¯ = z bar) 2. Evaluate the complex integral: ∫ C [iz^2 − z − 3i]dz, where C is the quarter circle with centre the origin which joins −1 to i.
Evaluate ∫∫∫T 2xy dx dy dz where T is the solid in the first octant bounded above by the cylinder z = 4 − x^2 below by the x, y-plane, and on the sides by the planes x =0, y = 2x and y = 4. Answer: ∫ (4, 0) ∫ (y/2, 0) ∫ (4−x^2, 0) 2xy dz dx dy = ∫ (2, 0) ∫ (4, 2x) ∫ (4−x^2, 0) 2xy dz dy dx = 128/3
is the Use Stokes' theorem to evaluate ſc(1+y)z dx + (1+z)x dy+(1 + x)y dz, where counterclockwise-oriented triangle with vertices (1,0,0), (0,1,0), and (0,0,1).
dz Consider the equation 6 sin(x + y) + 2 sin (x +z)+ sin(y +z)= 0. Find the values of and dz ду at the point (41,41,- 3x). dx dz cx (Simplify your answer. Type an exact answer, using radicals as needed.) (41,4x - 3x) dz dy (43,4%, - 3x) (Simplify your answer. Type an exact answer, using radicals as needed.)