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Find limit function ofThe 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 Consider Consider 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 Evaluate Evaluate Evaluate Evaluate Evaluate Evaluate x + y + z =1 1/24 Evaluate Evaluate Evaluate Evaluate Evaluate Evaluate Evaluate Evaluate Evaluate òòò zdxdydz if T is bounded by the planesx = 0, y = 0, z = 0, x + y + z =1 1/24 Evaluate 112/9 Evaluate òò ydxdy where G is a triangle with vertices O(0, 0), A(1, 1), B(0, 1) 1/3 Evaluate Evaluate Evaluate Evaluate Evaluate Evaluate Evaluate Evaluate Evaluate 3, 4). 13 Evaluate 1). 2 Evaluate Evaluate Evaluate= ò xyzdl , where L is a segment of the line between points A(1, 0, 1), B(2, 2, 3) 12 Evaluate Evaluate Evaluate Evaluate Evaluate 1). 1/12 Evaluate B(1, 1). -1/20 Evaluate 1). 17/30 Evaluate Evaluate Evaluate Evaluate Evaluate 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 = ez Find Find Find Find Find Find Find Find Find Find Find Find Find Find Find Find
Find angle between gradients of the functions Find arc length of the curve Find area bounded by the lemniscates Find area of the figure bounded by the curves Find area of the figure bounded by the curves Find derivative of the function Find derivative of the function Find derivative of the function Find derivative of the function Find derivative of the function 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 Find equation of tangent plane to the surface Find equation of tangent plane to the surface Find equation of tangent plane to the surface 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: Find the area bounded between two curves Find the area bounded between two curves: Find the area bounded between two curves: Find the area bounded between two curves: Find the area bounded between two curves: Find the area bounded between two curves: 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 Find volume of the body bounded by ellipsoid Find volume of the body bounded by the surfaces
Date: 2016-03-03; view: 1230
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given by 
, then 
given by 
, then 
given by 
, then 
if T is bounded by the planes 
if T is bounded by the surfaces 
if T is bounded by the surfaces 
if T is bounded by the surfaces 
Diverges
if T is bounded by the planes x = 0, y = 0, z = 0,
where G is a trapezoid with vertices A(1, 1), B(5, 1), C(10,2),D(2, 2) 112/9
where G is a triangle with vertices O(0, 0), A(1, 1), B(0, 1) 1/3
where G is bounded by the circle: 
where G is bounded by the circle: 
if T is bounded by the surfaces 
if T is bounded by the surfaces 
where G is a trapezoid with vertices A(1, 1), B(5, 1), C(10, 2), D(2, 2)
where G is bounded by the circle: 
where G is bounded by the circle: 
where G is bounded by the curves: 
where G is bounded by the curves: 
where G is bounded by the curves: 
where G is bounded by the curves: 
where C is a arch of the parabola y = x2 between points A(1, 1) and B(2, 4) 
, where C is a circle y2 + x2 = 4, moving in anticlockwise direction. 8Pi
where C is a segment of the line between points A(1, 1, 1) and B(2,
where C is arch of the parabola y = x2 between points A(-1,1) and B(1,
where L is a part of the circle: x2 + y2 = 9, x ³ 0, y ³ 0
, where L is a rectangle with vertices A(0, 0), B(4, 0), C(4, 2), D(0,2) 24
where L is a segment of the line y = 2x – 2 between points A(0, -2), B(1,0) 
, where L is a segment of the line y = x + 2 between points A(2, 4), B(1,3) 
where L is a segment of the line y = x/2 – 2 between points A(0, -2), B(4, 0) 
, where L is the first arch of the cycloid: x = a(t - sin t), y = a(1 - cos t), a>0 
where line C is given by the equation y = x2 between points A(0,0) and B(1,
where line C is given by the equation y = x3 between points A(0, 0) and
where line C is given by the equation y2 = x between points A(0, 0) and B(1,
where S is a part of the cone x2/16 + y2/16= z2/9 between planes z = 0 and z = 3 
where S is a part of the plane x + y + z = 1,x ³ 0, y ³ 0, z ³ 0. Sqrt3 /120
where S is a part of the surface x + 2y + z – 6 = 0, x ³ 0, y³ 0,z ³ 0. 54
where S is a part of the surface x2 + y2 = z2 between planes z = 0 and z = 2 
, where S is outside of the surface bounded by the planes x = 0, y = 0, z = 0 and x + 2y +3z = 6. 18
at the point 
cutting off by the line 
. 112/27
and 
and 
at M(1, 3, 2) by direction to the point N(0, 5, 0) 
at M(2, 1, 1) by direction of the vector a = -2i + j – k 
at M(-2, 3, 6) by direction to the point N(-1,1,4) 
at M(3, 4) by direction of the vector a(1, 1) 
at M(3, 4) by direction of the vector a(4, 3) 0
at the point M(1, 2,3) 
at the point 
at the point M(1,2, 3) 
32/3
9/2
256/3
8/3
125/3
128/15
16/15