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ked out of 6.00 Evaluate p Hay question Funds where F(x.y,z)=(xy, 292, 263-y-2)) and is the...
1 1 Consider the function f(x.y,z) 2x y 2 the point P(3,0,1), and the unit vector...
1 1 Consider the function f(x.y,z) 2x y 2 the point P(3,0,1), and the unit vector u 0 Compute the gradient of f and evaluate it at P b. Find the unit vector in the direction of maximum increase of f at P c. Find the rate of change of the function in the direction of maximum increase at P d. Find the directional derivative at P in the direction of the given vector. a.
1 1 Consider the function...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above th...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The value of the surface integral is (Type an exact answers, using t as needed.)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The...
1 30% For a paraboloid S: z(x.y)-x2+y, 0sz4 (a) (5%) Find a plane tangent to S at the point P(1, 1, 2) (b) (5%) Fin...
1 30% For a paraboloid S: z(x.y)-x2+y, 0sz4 (a) (5%) Find a plane tangent to S at the point P(1, 1, 2) (b) (5%) Find the direction where the derivative of S at P is the steepest (largest) (c) (5%) Find the unit shortest line one S that passes P () (d) (15 %) Determine the flux of F xi+ yj+ zk out of S. s (x, y) y X
1 30% For a paraboloid S: z(x.y)-x2+y, 0sz4 (a) (5%)...
Evaluate the surface integral s«w.vz) as where f(x, y, z) = x - y - zand...
Evaluate the surface integral s«w.vz) as where f(x, y, z) = x - y - zand o is the portion of the plane x + y = 1 in the first octant between 2 = 2 and 2 = 3. Enter the exact answer. f(x, y, z) ds = ? Edit 46.9.2) ds =
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk,...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
Find the directional derivative of f at p in the direction of a. f(x,y,z)=xy+z^2; P(2,-2,2);A=i+j+k
Find the directional derivative of f at p in the direction of a. f(x,y,z)=xy+z^2; P(2,-2,2);A=i+j+k
Question 2: Evaluate SS xy dA where D is the triangle in the (x, y) plane...
Question 2: Evaluate SS xy dA where D is the triangle in the (x, y) plane bounded by the lines y=x, x-5 and y=2. [10 points)
5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0 < y < 2 oriented by the unit no...
5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0 < y < 2 oriented by the unit normal pointing out of the cylinder.
5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0
F.df, where F(x, y, z) = (yz, uz, xy), and C is ANY smooth path from...
F.df, where F(x, y, z) = (yz, uz, xy), and C is ANY smooth path from (0,0,0) to 11. a) Evaluate (2, -1, -2). b) If a particle sat at (0,0,0), give a possible physical interpretation of the line integral you com puted.
1 1 Consider the function f(x.y,z) 2x y 2 the point P(3,0,1), and the unit vector u 0 Compute the gradient of f and evaluate it at P b. Find the unit vector in the direction of maximum increase of f at P c. Find the rate of change of the function in the direction of maximum increase at P d. Find the directional derivative at P in the direction of the given vector. a.
1 1 Consider the function...
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The value of the surface integral is (Type an exact answers, using t as needed.)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The...
1 30% For a paraboloid S: z(x.y)-x2+y, 0sz4 (a) (5%) Find a plane tangent to S at the point P(1, 1, 2) (b) (5%) Find the direction where the derivative of S at P is the steepest (largest) (c) (5%) Find the unit shortest line one S that passes P () (d) (15 %) Determine the flux of F xi+ yj+ zk out of S. s (x, y) y X
1 30% For a paraboloid S: z(x.y)-x2+y, 0sz4 (a) (5%)...
Evaluate the surface integral s«w.vz) as where f(x, y, z) = x - y - zand o is the portion of the plane x + y = 1 in the first octant between 2 = 2 and 2 = 3. Enter the exact answer. f(x, y, z) ds = ? Edit 46.9.2) ds =
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
Question 2: Evaluate SS xy dA where D is the triangle in the (x, y) plane bounded by the lines y=x, x-5 and y=2. [10 points)
5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0 < y < 2 oriented by the unit normal pointing out of the cylinder.
5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0
F.df, where F(x, y, z) = (yz, uz, xy), and C is ANY smooth path from (0,0,0) to 11. a) Evaluate (2, -1, -2). b) If a particle sat at (0,0,0), give a possible physical interpretation of the line integral you com puted.
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