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

Considergiven by, then

Considergiven by, then

Considergiven 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

Evaluateif T is bounded by the planes

Evaluateif T is bounded by the surfaces

Evaluateif T is bounded by the surfaces

Evaluateif T is bounded by the surfaces

Evaluate

EvaluateDiverges

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

x + y + z =1 1/24

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

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

Evaluatewhere G is bounded by the circle:

Evaluatewhere G is bounded by the circle:

Evaluateif T is bounded by the surfaces

Evaluateif 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

Evaluatewhere 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

Evaluatewhere G is bounded by the circle:

Evaluatewhere G is bounded by the circle:

Evaluatewhere G is bounded by the curves:

Evaluatewhere G is bounded by the curves:

Evaluatewhere G is bounded by the curves:

Evaluatewhere G is bounded by the curves:

Evaluatewhere 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

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

3, 4). 13

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

1). 2

Evaluatewhere 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

Evaluatewhere 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)

Evaluatewhere 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

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

1). 1/12

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

B(1, 1). -1/20

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

1). 17/30

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

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

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

Evaluatewhere 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 d^{2}z/dx^{2} 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 functionsat the point

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

Find area bounded by the lemniscates

Find area of the figure bounded by the curvesand

Find area of the figure bounded by the curvesand

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

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

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

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

Find derivative of the functionat 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 surfaceat the point M(1, 2,3)

Find equation of tangent plane to the surfaceat the point

Find equation of tangent plane to the surface

Find equation of tangent plane to the surfaceat 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

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables:

Find the partial derivative z(x)of the function of two variables

Find the partial derivative z(x)of the function of two variables

Find the partial derivative z(x)of the function of two variables

Find the partial derivative z(x)of the function of two variables

Find the series radius and interval convergence, if the formula for the n-th term is

Find the series radius and interval of convergence, if the formula for the n-th term is 𝐧𝐱𝐧/(𝐧 + 𝟒) 1,

Find the sum of series

Find the sum of series

Find the volume of the solid, formed by x-axial rotation of curvilinear trapezoid, bounded by the lines

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