Find limit function of

The first octant 0

Compute flux for the vector fieldF = (x - 3z)i + (x + 2y + z) j + (4x + y)k by upper part of the plane x+ y + z = 2 located in the first octant 28/3

A. Compute flux of the vector fieldF = 3xi + (y + z) j + (x - z)k by the outer surface of pyramid bounded by plane x + 3y + z = 3 and coordinate planes 9/2

Compute flux of the vector fieldF = (3x -1)i + (y - x + z) j + 4zk by the outer surface of pyramid bounded by plane 2x - y - 2z = 2 and coordinate planes 8/3

Compute flux of the vector fieldF = (2y + z)i + (x - y) j - 2zk by the outer surface of pyramid bounded by plane x - y + z = 2 and coordinate planes -4

Consider given by , then

Consider given by , then

Consider given by , then

Criterion of Riemann integrablity of the function: (" e >0) ($P - partition) U(f, P) - L(f, P) <e

Determine the interval of convergence of the following power series:

Evaluate

Evaluate if T is bounded by the planes

Evaluate if T is bounded by the surfaces

Evaluate if T is bounded by the surfaces

Evaluate if T is bounded by the surfaces

Evaluate

Evaluate Diverges

Evaluate if T is bounded by the planes x = 0, y = 0, z = 0,

x + y + z =1 1/24

Evaluate where G is a trapezoid with vertices A(1, 1), B(5, 1), C(10,2),D(2, 2) 112/9

Evaluate where G is a triangle with vertices O(0, 0), A(1, 1), B(0, 1) 1/3

Evaluate where G is bounded by the circle:

Evaluate where G is bounded by the circle:

Evaluate if T is bounded by the surfaces

Evaluate if T is bounded by the surfaces

Evaluate

Evaluate

Evaluate òòò zdxdydz if T is bounded by the planesx = 0, y = 0, z = 0, x + y + z =1 1/24

Evaluate where G is a trapezoid with vertices A(1, 1), B(5, 1), C(10, 2), D(2, 2)

112/9

Evaluate òò ydxdy where G is a triangle with vertices O(0, 0), A(1, 1), B(0, 1) 1/3

Evaluate where G is bounded by the circle:

Evaluate where G is bounded by the circle:

Evaluate where G is bounded by the curves:

Evaluate where G is bounded by the curves:

Evaluate where G is bounded by the curves:

Evaluate where G is bounded by the curves:

Evaluate where C is a arch of the parabola y = x2 between points A(1, 1) and B(2, 4)

Evaluate , where C is a circle y2 + x2 = 4, moving in anticlockwise direction. 8Pi

Evaluate where C is a segment of the line between points A(1, 1, 1) and B(2,

3, 4). 13

Evaluate where C is arch of the parabola y = x2 between points A(-1,1) and B(1,

1). 2

Evaluate where L is a part of the circle: x2 + y2 = 9, x ³ 0, y ³ 0

Evaluate , where L is a rectangle with vertices A(0, 0), B(4, 0), C(4, 2), D(0,2) 24

Evaluate= ò xyzdl , where L is a segment of the line between points A(1, 0, 1), B(2, 2, 3) 12

Evaluate where L is a segment of the line y = 2x – 2 between points A(0, -2), B(1,0)

Evaluate , where L is a segment of the line y = x + 2 between points A(2, 4), B(1,3)

Evaluate where L is a segment of the line y = x/2 – 2 between points A(0, -2), B(4, 0)

Evaluate , where L is the first arch of the cycloid: x = a(t - sin t), y = a(1 - cos t), a>0

Evaluate where line C is given by the equation y = x2 between points A(0,0) and B(1,

1). 1/12

Evaluate where line C is given by the equation y = x3 between points A(0, 0) and

B(1, 1). -1/20

Evaluate where line C is given by the equation y2 = x between points A(0, 0) and B(1,

1). 17/30

Evaluate where S is a part of the cone x2/16 + y2/16= z2/9 between planes z = 0 and z = 3

Evaluate where S is a part of the plane x + y + z = 1,x ³ 0, y ³ 0, z ³ 0. Sqrt3 /120

Evaluate where S is a part of the surface x + 2y + z – 6 = 0, x ³ 0, y³ 0,z ³ 0. 54

Evaluate where S is a part of the surface x2 + y2 = z2 between planes z = 0 and z = 2

Evaluate , where S is outside of the surface bounded by the planes x = 0, y = 0, z = 0 and x + 2y +3z = 6. 18

Evaluate

Evaluate definite integral:

Evaluate the double integral:

Evaluate the indefinite integral:

Evaluate:

Find dz/dx at (1, -2, 2), if

Find dz/dy at (1, -2, 2), if

Find d²z/dx² if x+y+z = e^z

Find

Find

Find

Find

Find

Find

Find

Find

Find

Find

Find

Find

Find

Find

Find

Find

Find angle between gradients of the functions at the point

Find arc length of the curve cutting off by the line . 112/27

Find area bounded by the lemniscates

Find area of the figure bounded by the curves and

Find area of the figure bounded by the curves and

Find derivative of the function at M(1, 3, 2) by direction to the point N(0, 5, 0)

Find derivative of the function at M(2, 1, 1) by direction of the vector a = -2i + j – k

Find derivative of the function at M(-2, 3, 6) by direction to the point N(-1,1,4)

Find derivative of the function at M(3, 4) by direction of the vector a(1, 1)

Find derivative of the function at M(3, 4) by direction of the vector a(4, 3) 0

Find domain of the function

Find domain of the function

Find domain of the function

Find domain of the function

Find domain of the function

Find dominating series for the series

Find dominating series for the series

Find dominating series for the series

Find equation of normal line to the surface

Find equation of normal line to the surface

Find equation of normal line to the surface at the point M(1, 2,3)

Find equation of tangent plane to the surface at the point

Find equation of tangent plane to the surface

Find equation of tangent plane to the surface at the point M(1,2, 3)

Find grad u at the point M(1, -1, -1), if

Find grad u at the point M(1, 1, 1), if

Find grad u at the point M(1, -1, 2), if

Find grad u at the point M(-1, 2, 1), if

Find grad u at the point M(3, 0, 2), if

Find grad u at the point M(3, 4, -1), If

Find interval of uniformly convergence of functional series:

Find limit function of

Find points of discontinuity of

Find points of discontinuity of

Find points of discontinuity of

Find radius of convergence of power series:

Find radius of convergence of power series:

Find radius of convergence of power series:

Find radius of convergence of power series:

Find sum of the series

Find sum of the series

Find sum of the series

Find the area between the line x = 2 and the curves f(x) = x(x-2) and g(x)=x/2. 7/3

Find the area bounded between two curves: 32/3

Find the area bounded between two curves

Find the area bounded between two curves:

Find the area bounded between two curves: 9/2

Find the area bounded between two curves: 256/3

Find the area bounded between two curves: 8/3

Find the area bounded between two curves: 125/3

Find the area bounded between two curves:

Find the area bounded by the lines x = 0,x =p , y = 0 andy = cosx 2

Find the area bounded by the linesx = 0,y = 2 and

Find the area of an ellipsepab

Find the common term of the number series:

Find the common term of the number series:

Find the common term of the number series:

Find the interval of convergence of the power series

Find the length of the cardioid: r = 2a(1-cosq) 16a

xy=6, x=1, x=6.30p

Find the volume of the solid, formed by x-axial rotation of figure, bounded by the line x4+y4=a2x2

Find the volume of the solid, formed by x-axial rotation of figure, bounded by the line x4+y4=x3

Find volume of the body bounded by ellipsoid

Find volume of the body bounded by the surfaces

128/15

16/15

Date: 2016-03-03; view: 1518