(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to th...
Let E be the solid bounded by y+z=1 z=0 and y=x^2 a) Bind z, and provide (but do not evaluate) the triple integral with the plane described horizontally simple (dz dx dy) b) Bind z, and provide (but do not evaluate) the triple integral with the plane described vertically simple (dz dy dx) c) Bind x, and provide (but do not evaluate) the triple integral with the plane described horizontally simple (dx dy dz) d) Bind x, and provide (but...
U Question 15 "C 7 pts "С If S is the surface of the cylinder E= {(x,y,z) : 32 + y < 4,1523}, oriented outwards, which of the following (after applying the Divergence Theorem) will compute zyz) - dS? 40 O (1 + y2 cos & sin 6)r dr de dz REC O 1988 6%" /*(1 + == sin ®)r dr do dz %%% %%% %%% (r cos 0 + 32 + y2 z cos ( sin 0), dr do...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
Let C1 be the semicircle given by z = 0,y ≥ 0,x2 + y2 = 1 and C2 the semicircle given by y = 0,z ≥ 0,x2 +z2 = 1. Let C be the closed curve formed by C1 and C2. Let F = hy + 2y2,2x + 4xy + 6z2,3x + eyi. a) Draw the curve C. Choose an orientation of C and mark it clearly on the picture. b) Use Stokes’s theorem to compute the line integral ZC...
Let Select all that apply Let z =f(x,y)= arctan(3x In(6) Select all that apply Your answer: The slope of the tangent line to the curve obtained by intersecting the 9 surface z =f(x,y) and plane x = 3 at the point (3,6) is 6(811n (36) + 1) + fxy 54x2In(6y)+3) y(18x2in(6) + 1)2 (fxx (4,2))-(fvx(4,2)) = 0 The slope of the tangent line to the curve obtained by intersecting the 3In(36) surface z = f(x,y) and plane x = 3 at...
e.) What is the equation of the tangent plane to the function z = x2 + 4y2 at the point with x = 2, y = -1? [8 points) f.) For the curve through space F(t) =< sin(3t), cos(3t), 2t>, what is the unit tangent vector at t = 7/2? [8 points] g.) Starting from t= 0, reparameterize the curve r(t) = (1 - 2t) î +(-4+ 2t)ſ+(-3 – t)k in terms of arclength. [8 points]
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...
Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (0, 0, 0), (2, 1, 5), (1, 1, 3), and back to the origin, in that order. Use Stokes' theorem to evaluate the integral: (Use symbolic notation and fractions where needed.) (xyz) dx + (3xy) dy + (x) dz = D .
Please try helping with all three questions.......please 1 point) Integratef(x, y, z) 6xz over the region in the first octant (x,y, z 0) above the parabolic cylinder z = y2 and below the paraboloid Answer Find the volume of the solid in R3 bounded by y-x2 , x-уг, z-x + y + 24, and Z-0. Consider the triple integral fsPw xyz2 dV, where W is the region bounded by Write the triple integral as an iterated integral in the order...
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....