Filters
Question type

Determine whether or not vector field is conservative. If it is conservative, find a function f such that F=f.\mathbf { F } = \nabla f . F(x,y,z)=35yze5xzi+7e5xzj+35xye5xzk\mathbf { F } ( x , y , z ) = 35 y z e ^ { 5 x z } \mathbf { i } + 7 e ^ { 5 x z } \mathbf { j } + 35 x y e ^ { 5 x z } \mathbf { k }

Correct Answer

verifed

verified

Evaluate the surface integral. Round your answer to four decimal places. S3zdS\iint _ { S } 3 z d S S is surface x=y2+2z2,0y1,0z1x = y ^ { 2 } + 2 z ^ { 2 } , 0 \leq y \leq 1,0 \leq z \leq 1


A) 10.596310.5963
B) 13.596313.5963
C) 4.59634.5963
D) 23.596323.5963
E) 8.59638.5963

F) D) and E)
G) A) and B)

Correct Answer

verifed

verified

Find the gradient vector field of f(x,y,z)=xcos2y9zf ( x , y , z ) = x \cos \frac { 2 y } { 9 z }

Correct Answer

verifed

verified

Evaluate the line integral over the given curve C. C3y2zds\int _ { C } 3 y ^ { 2 } z d s ; C:r(t) =10ti+sin7tj+cos7tkC : \mathbf { r } ( t ) = 10 t \mathbf { i } + \sin 7 t \mathbf { j } + \cos 7 t \mathbf { k } , 0tπ20 \leq t \leq \frac { \pi } { 2 }


A) 17- \frac { 1 } { 7 } 149\sqrt { 149 }
B) 3
C) 1
D) 1497π\frac { \sqrt { 149 } } { 7 } \pi

E) All of the above
F) C) and D)

Correct Answer

verifed

verified

Evaluate Cxy4dS\int _ { C } x y ^ { 4 } d S where C is the right half of the circle x2+y2=9x ^ { 2 } + y ^ { 2 } = 9


A) 293.6293.6
B) 292.6292.6
C) 291.6291.6
D) 295.6295.6
E) 294.6294.6

F) C) and E)
G) B) and C)

Correct Answer

verifed

verified

Match the vector field with its plot. F(x,y) =xx2+y2iyx2+y2j\mathbf { F } ( x , y ) = \frac { x } { x ^ { 2 } + y ^ { 2 } } \mathbf { i } - \frac { y } { x ^ { 2 } + y ^ { 2 } } \mathbf { j }


A)  Match the vector field with its plot.  \mathbf { F } ( x , y )  = \frac { x } { x ^ { 2 } + y ^ { 2 } } \mathbf { i } - \frac { y } { x ^ { 2 } + y ^ { 2 } } \mathbf { j }  A)    B)    C)    D)
B)  Match the vector field with its plot.  \mathbf { F } ( x , y )  = \frac { x } { x ^ { 2 } + y ^ { 2 } } \mathbf { i } - \frac { y } { x ^ { 2 } + y ^ { 2 } } \mathbf { j }  A)    B)    C)    D)
C)  Match the vector field with its plot.  \mathbf { F } ( x , y )  = \frac { x } { x ^ { 2 } + y ^ { 2 } } \mathbf { i } - \frac { y } { x ^ { 2 } + y ^ { 2 } } \mathbf { j }  A)    B)    C)    D)
D)  Match the vector field with its plot.  \mathbf { F } ( x , y )  = \frac { x } { x ^ { 2 } + y ^ { 2 } } \mathbf { i } - \frac { y } { x ^ { 2 } + y ^ { 2 } } \mathbf { j }  A)    B)    C)    D)

E) A) and B)
F) A) and C)

Correct Answer

verifed

verified

Find the work done by the force field F(x,y) =xsin(y) i+yj\mathbf { F } ( x , y ) = x \sin ( y ) \mathbf { i } + y \mathbf { j } on a particle that moves along the parabola y=x2 from (1,1)  to (2,4) y = x ^ { 2 } \text { from } ( 1,1 ) \text { to } ( 2,4 )


A) (17cos(1) +cos(4) ) 2\frac { ( 17 - \cos ( 1 ) + \cos ( 4 ) ) } { 2 }
B) (15+cos(1) cos(4) ) 2\frac { ( 15 + \cos ( 1 ) - \cos ( 4 ) ) } { 2 }
C) (15+sin(1) sin(4) ) 2\frac { ( 15 + \sin ( 1 ) - \sin ( 4 ) ) } { 2 }
D) (15+sin(1) cos(4) ) 2\frac { ( 15 + \sin ( 1 ) - \cos ( 4 ) ) } { 2 }
E) (17+cos(1) cos(4) ) 2\frac { ( 17 + \cos ( 1 ) - \cos ( 4 ) ) } { 2 }

F) B) and C)
G) B) and D)

Correct Answer

verifed

verified

Let F be a vector field. Determine whether the expression is meaningful. If so, state whether the expression represents a scalar field or a vector field. curl (div F)

Correct Answer

verifed

verified

div F is a scalar fi...

View Answer

Find the area of the surface S where S is the part of the surface x=yzx = y z that lies inside the cylinder y2+z2=16y ^ { 2 } + z ^ { 2 } = 16

Correct Answer

verifed

verified

Find a function f such that F=f\mathbf { F } = \nabla f , and use it to evaluate CFdr\int _ { C } \mathbf { F } \cdot d \mathbf { r } along the given curve C. F(x,y)=e6yi+(1+6xe6y)j,C:r(t)=teti+(1+t)j,0t1\mathbf { F } ( x , y ) = e ^ { 6 y } \mathbf { i } + \left( 1 + 6 x e ^ { 6 y } \right) \mathbf { j } , \quad C : \mathbf { r } ( t ) = t e ^ { t } \mathbf { i } + ( 1 + t ) \mathbf { j } , 0 \leq t \leq 1

Correct Answer

verifed

verified

Let r=xi+yj+zk and r=r\mathbf { r } = x \mathbf { i } + y \mathbf { j } + z \mathbf { k } \text { and } r = | \mathbf { r } | \text {. }  Find (8rr)\text { Find } \nabla \cdot ( 8 r \mathbf { r } )

Correct Answer

verifed

verified

Find an equation in rectangular coordinates, and then identify the surface. r(u,v)=6vi+(8uv)j+(u+6v)kr ( u , v ) = 6 v \mathbf { i } + ( 8 u - v ) \mathbf { j } + ( u + 6 v ) \mathbf { k }

Correct Answer

verifed

verified

The plot of a vector field is shown below. A particle is moved  from the point \text { from the point } (3,3)( 3,3 )  to \text { to } (0,0)( 0,0 ) . By inspection, determine whether the work done by F on the particle is positive, negative, or zero.  The plot of a vector field is shown below. A particle is moved  \text { from the point }   ( 3,3 )   \text { to }   ( 0,0 )  . By inspection, determine whether the work done by F on the particle is positive, negative, or zero.

Correct Answer

verifed

verified

A thin wire is bent into the shape of a semicircle x2+y2=4,x>0x ^ { 2 } + y ^ { 2 } = 4 , x > 0 If the linear density is 44 , find the exact mass of the wire.


A) 3π3 \pi
B) 18π18 \pi
C) 8π8 \pi
D) 8π28 \pi ^ { 2 }
E) 2π2 \pi

F) B) and E)
G) A) and B)

Correct Answer

verifed

verified

Find a parametric representation for the part of the elliptic paraboloid x+y2+2z2=7x + y ^ { 2 } + 2 z ^ { 2 } = 7 that lies in front of the plane x = 0.


A) x=7y22z2,y=y,z=y,y2+2z27x = 7 - y ^ { 2 } - 2 z ^ { 2 } , y = y , z = y , y ^ { 2 } + 2 z ^ { 2 } \leq 7
B) x=x,y=7x+2z2,z=zx = x , y = \sqrt { 7 - x + 2 z ^ { 2 } } , z = z
C) x=x,y=±7x+2z2,z=zx = x , y = \pm \sqrt { 7 - x + 2 z ^ { 2 } } , z = z
D) x=7y22z2,y=y,z=y,0y2+2z23x = 7 - y ^ { 2 } - 2 z ^ { 2 } , y = y , z = y , 0 \leq y ^ { 2 } + 2 z ^ { 2 } \leq 3
E) x=7y22z2,y=y,z=y,y2+2z27x = 7 - y ^ { 2 } - 2 z ^ { 2 } , y = y , z = y , y ^ { 2 } + 2 z ^ { 2 } \geq 7

F) B) and D)
G) C) and E)

Correct Answer

verifed

verified

Determine whether F is conservative. If so, find a function f such that F=f.\mathbf { F } = \nabla f . . F(x,y,z)=(6sinh2z)i+(3e5zcos3y)j+(12xcosh2z)k\mathbf { F } ( x , y , z ) = ( 6 \sinh 2 z ) \mathbf { i } + \left( 3 e ^ { 5 z } \cos 3 y \right) \mathbf { j } + ( 12 x \cosh 2 z ) \mathbf { k }

Correct Answer

verifed

verified

The vector field
blured image
i...

View Answer

Evaluate the surface integral SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S } for the given vector field F and the oriented surface S. In other words, find the flux of F across S. F(x,y,z)=xizj+yk, Sis the sphere x2+y2+z2=25\mathbf { F } ( x , y , z ) = x \mathbf { i } - z \mathbf { j } + y \mathbf { k } , \text { Sis the sphere } x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25 in the first octant, with orientation toward the origin.

Correct Answer

verifed

verified

Showing 121 - 137 of 137

Related Exams

Show Answer