7. If F = (yz,-2xz,xy), the value of ||F.n dS , where S is a sphere of radius a centered at the origin, is (a) 0. (b) 2z. (c) 4.

Q: 1. Use an antiderivative to show that for every contour C extending from a point z₁ to a point 22, 1…

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Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

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Q: 10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

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Q: Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

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Q: What is the largest vertical distance between the graphs of the functions y = Va and y x2 in the…

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Q: Evaluate the line integral x +1 ds /1+4x² Vĩ where C is the part of the parabola y = 9 – x² from…

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Q: What is the area of the triangle bounded by the x and y axes and the tangent to the curve xy^2=4 at…

A: xy2=4 Differentiating with respect to x, we get…

Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

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Q: 7. Find the area of the surfaces generated by revolving the curve r = 2e®² for 0<0s- about x- axis.

A: The solution are next step..

Q: 6) What is the tangent plane of f (x, y) = 5x² – 2xy? + 3xy + 4x at point (xo, Yo) = (1, –2) ?

A: The question is solved in step. 2

Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.

Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

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Q: 4 Find the curvature k of the plane curve y = x +- at x = 1. K =

A: Given curve is , y= x + 4x  at x=1

Q: Find a formula for a functionf(x, y, z) whose level surface f= 3 is a cylinder of radius 5 centered…

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Q: 4. Let f(z) = 1 23 1 - and find [ f(z) dz, where C a circle of radius 2 about the origin with…

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Q: DNE.) +2+ f defined on |-1,3] maximum (x, y) = minimum (x, y) = Need Helo?

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Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: # 4. Evaluate the line integral | (x +2x²y) ds, where C is the upper half of the unit circle x2 + y2…

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Q: 9) Find a point on the surface z= 8 – 3x² – 2y² at which the tangent plane is perpendicular to the…

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Q: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…

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Q: Find the maximum and minimum values attained by f(x,y,z) = xyz on the unit ball x2+y2+z2 ≤ 1

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Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

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Q: a) Evaluate the line integral S. (2x – y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

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Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

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Q: 2.7 Describe cll soilutions of Asso where A is the Yow ta the matirix meg Vse Y S, and/or t as in…

A: Given  A=1-6-50-2-100100-200001-7000000 Here, we have to solve Ax=0

Q: Compute 6xy da dy, where D is bounded by the curves y = 4 – x2 and y = 2x + 4.

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Q: The area enclosed between the curves p(a) =2 +*+ 3 and g(@) = -22 - * + is O 16 47 %3D 18 49 O -49…

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Q: 3. Find the extreme values of the given f(x, y) on the indicated surface. f (x, y) = 8x² – 2y; x² +…

A: The solution of the problem is given in the next step.

Q: (3) +. R Ris bounded by the semicircle y = V2x – x² and the line y = x

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Q: 4. Evaluate ||| x y dV , where E is bounded by the parabolic cylinders y = x², y' = x and the planes…

A: The region E is bounded by the parabolic cylinders y = x2, x = y2 and the planes z = 0 and z = x +…

Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

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Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

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Q: Find the line integral (4х — 5у) ds, where C is the semicircle y = 9 – x² traversed from (3,0) to…

A: Graph the semi-circle. Take x=3cost and y=3sint Now, x'=-3sint and y'=3cost The angle covered by…

Q: 20- What is the share of the formula that allows calculating the y coordinate of the center of…

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Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

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Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

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Q: Suppose that the Celsius temperature at the point (x,y,z) on the sphere x +y +z =1 is T= 1600xyz“.…

A: This is a problem related to maxima and minima. Based on the general formula we will answer the…

Q: 4. Find the area of the surface generated by revolving the given curve about the -axis. y = 7x,0 <…

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Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

Q: Find the radius R, of curvature to the hyperbola y = x + 3x² – x³ at the point x = 0 given that R =…

A: To find the radius R, of curvature to the given hyperbola at point x = 0.