Q2. The Normal at a point P of ellipsoid + f² = 1 meets the coordinate's d2 planes in D1, D2, D3 , prove that the ratios PD1,PD2, PD3 are constants.

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x2-c2 and y=c2-x2…

A:

Q: If (a,ß.r) is a point at which the surface x2+y2-z-2x+42=0 has a horizontal tangent plane, then Iyl=

A: Horizontal tangent plane

Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

A:

Q: 1. Find Sp(r+2y)dA, where D is the region bounded by the parabolas y = r2, and y=1+2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Let C be the curve y 8ī for 1.5 < T < 3.6. %3D 16 15 14 13 12 10 Find the surface area of revolution…

A: the given curve is take derivative

Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

A:

Q: Consider the ellipsoid 4x? + y?+ 222 = 25. Find all the points where the tangent plane to this…

A:

Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

A:

Q: 28. F(x, y, z) = x³i+y°j+z°k, and S is the sphere of radius 3 and centered at the origin.

A: divF→=ddxx3+ddyy3+ddzz3        =3x2+3y2+3z2        =3x2+y2+z2  by divergence theorem,…

Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent is constant and the…

A: The given curve is y=bexa.

Q: 4. if (r+r³)d m is the x coordinate of the center of mass of a rectangular sheet R with m being the…

A:

Q: The plane x+ y = 1 intersects the paraboloid z = in a parabola. Parametrize the whole parabola using…

A:

Q: Q3. A- Use Greens theorem to evaluate the cireulation or flus for the velocity fiekd : S(x, y)=- *+y…

A: Given velocity field is  f(x,y)=1x+yi-1x+yj we have to find the flux for the boundary of square…

Q: Q2 (a) Find the volume under the surface z = 3x3 + 3x²y and over the rectangle R = {(x,y):1 < x <…

A:

Q: Let L be the tangent line to the hyperbola xy = 1 at x = a, where a &gt; 0. Show that the area of…

A:

Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the…

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: If F = (2z+ y,z, 2y+x) and S is a unit square in the yz-plane with its normal in the positive…

A: Consider the given vector F.

Q: Evaluate the integral | (3x – 2 y + :)ds where C is the curve, C, and C, as shown. 3- y² + z² 2. 3…

A: Here, Curve C is equivalent to c1+c2. The point of intersections of c1 and c2 is at 0,1,0.

Q: If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A:

Q: If the maximum distance from the surface x? + 2y² + z? = 3 to the point (1,0, –1) is Va+ bv6, what…

A:

Q: PICTURE

A: We are given that the cone ax2+by2+z2 = 0 and the ellipsoid 2x2+4y2+z2 = 42 intersect and are…

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x^2 - c^2 and…

A: Given: The given parabolas are y=x2-c2 and y=c2-x2. Determine the points of intersection.…

Q: Evaluate the integral [(3x – 2y + z)ds where C is the curve, C, and C, as shown. 3 y²+ z² 2 G 2* 3…

A: Given that ∫c3x-2y+zds. The objective is to find the integral value. ∫c3x-2y+zds=∫c13x-2y+z…

Q: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

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

A:

Q: Find the average height of the paraboloid z = x2 + y2 over the square 0&lt;= x &lt;= 2, 0…

A:

Q: If the infinite curve  y = e−8x, x ≥ 0,  is rotated about the x-axis, find the area of the…

A: Given: y=e-8x , x≥0

Q: The volume of the solid generated by the curve y = e 2, between z = 2 and z = 6 about the a - aris…

A: Solution-

Q: Q4: Calculate the integral . F.dr , where F 2xy i+ x²j, if the curve c, lying in the plane XY, is:…

A:

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: 2. At what point on z = a? + y? is the tangent plane parallel to 3.r – 4y + z = 7 ?

A:

Q: Graph the surface 1 = y? +z? - by first sketching at least three cross sections in each of the xy…

A:

Q: Given the area bounded by the parabola x² – 4x + 12y- 20 = 0, the x- axis and the lines x = 1 and x…

A: Sol

Q: Q4(a) Find the surface area of the part of the paraboloid z=10-x -y' that lies above the plane :=1.

A:

Q: Let C be the curve y = 9/ for 1.3 < 3.4. 16 +15 14 12 -구 Find the surface area of revolution about…

A:

Q: For the ellipsoid 2.x2 + 3y? + 422 = 50, %3D find normals and tangent planes in the points where the…

A:

Q: At which of the points below is the tangent plane to the surface r2 – 2y? + z2 + yz = 2 vertical?…

A: From the tangent plane to a surface

Q: Find the area of the surface generated when the given curve is revolved about the y-axis. y= (3x/3,…

A: Note: "Since you have asked multiple questions, we will solve the first question for you. If you…

Q: XII. $F•d$ where F = (x,y,z²) and S is sphere of radius 2 with center at 0.

A: F→=x,y,z2, surface S is sphere of radius 2 with centre O=0,0,0To find: ∯SF→.dS→

Q: Let C be the curve y = 5/a for 2.6 < a < 4.7. %3D 10 4 3 4. Find the surface area of revolution…

A: Function  y=5x for 2.6≤x≤4.7Formula→Surface area about x-axisS=∫ab2πy1+dydx2dx,  a≤x≤b

Q: find the Jolume of the salid genereted by revaling- the curve 4t'qy=36 between y = 0. and g=2 Gbout…

A: The objective is to find the volume of the solid about y-axis.

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: Line integrals

Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: B. Let C be the curve y = 1 – x2, 0< x < 1. If C is rotated about the y axis find the area of the…

A: our objective is to calculate the surface area.

Q: The tangent plane to the graph of the surface z=In(x<+y<) at the point (1,0,0) contains point…

A: and point (1,0,0)

Q: Find a cubic approximation of r(θ) = (θ 2 , eθ , θ) at θ = 0.

A: given rθ=θ2,eθ,θ to find - cubic approximation at θ=0

Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

A:

Q: Let C be the curve of intersection of the cylinder x2+y? = 2 and the hyperbolic paraboloid x? – y? +…

A:

Q: Show that at any point (x,y) on the curve y = be", the length of the subtangent is constant and the…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.