sin (z) cos3 (z) dz. y° cos (3y) dy. sin (z) cos3 (z) dz. y° cos (3y) dy.
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0
4. (a Let (sin( x cos( ) dr...
23 y?z? sin(x4) dx dy dz
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) -...
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.)
Use the Chain Rule to find dz/dt. z = sin(x) cos(y), x= VE, y = 7/t dz dt 11
The figure shows the region of integration for the integral. fx, y, z dy dz dx 0 Jo Rewrite this integral as an equivalent iterated integral in the five other orders. (Assume yx) 6x and z(x)-36-) x. f(x, y, 2) dy dx dz x, , z) dz dx dy f(x, y, z) dz dy dx f(x, y, z) dx dy dz fx, y, z) dx dy dz J0 Jo Jo f(x, y, z) dz dx dy 0 0 f(x, y,...
Problem 18. 7/2 (1 point) Evaluate the iterated integral AIT cos(x+y+z) dz dx dy. Answer:
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
5. (4 points) Calculate integral $.264 + z sin y)dx + (x? cos y − 3yjº)dy along triangle with vertices (0,0), (1,0) and (1,1), oriented counterclockwise, using Green's theorem.
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...