4x2 dx - xy dy 16x2, y = o from (-1, 0, 16) to (1, 0, 16) (d) dz, where c is the parabola z

Q: Q4/ Find the abs.max cand abs, min Valuse of the Runctia Kcx, y) = I+xy-3x on the closed regen…

A: We have f(x, y) = 1+xy-3x ∂f∂x = y-3, ∂f∂x = 0, y-3 = 0, y = 3 ∂f∂y = x, ∂f∂y = 0, x=0 So one…

Q: 2x2 dv, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0,…

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Q: Sketch the surfaces CYLINDERS z = y2 - 1

A: We need to sketch the surface formed by the function

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

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Q: Find the dimensions of the largest rectangular box in the first octant (x, y, z > 0) with one corner…

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Q: Find the points on the surface x² + y² + z² = 4 farthest from the point (1,–1,1), 2 %D

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Q: Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.

A: Given, the cylinder                         We have to find a parameterization of this given…

Q: 4. Where does the curve r(t) = ti + t²j+ (3 t2)k intersect the paraboloid z = x2 +y² ?

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Q: c) x+2y) dA, where D is bounded by the parabolas y=2x2 and y =1+x?.

A: C) The area D bounded by the parabolas y=2x2 & y=1+x2 is as shown below. The red graph is of…

Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

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Q: F = [y3,n3] 4 c is the Parrabola y - sa2 from A (0,0) +0 Bl2,20) SF.di = Syoda tao dy y=5a2 Since y…

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Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: .. Evaluate (x+y) dx+xy dy where C is the parabola y = x², x : 0 → 2.

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Q: J (2x+y) dx + (x+2y) dy L is circle of center (7,8) and radius 9

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Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

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Q: Calculate 127 y [1/10 ds where C is the parabola r(t) = (t, t², 0). Let 1 ≤ t ≤ 4. X

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Q: valuate f (z) dz.where C is the parabola y =x2 from z =-1+i ti 7 = 1+i and S (z ) = 6.x

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Q: Find the greatest and smallest values that the function f(x,y) = 4xy takes on the ellipse x +2y² = 1…

A: Let's find.

Q: Find the points on the surface z2 = xy + 4 closest to the origin.

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Q: 8. Calculate fo F • dr, where F(x, y) = y² i + (6x + 6y)j, and C is the portion of the parabola 2y²…

A: Given curve is 2y2-x=1 and points are (1,-1) to (7,2)

Q: 3) For the parametric system, find dy d2y When is the graph concave up or down? and dx dx2 x = t2 -…

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Q: Find the equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

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Q: Vf(x, y) = 4y sin(xy)i + 4x sin(xy)j, F = V f(x,y), and C' is the segment of the parabola y = 5x²…

A: According to the fundamental theorem of line integral, for a smooth curve C given by r→t, a≤t≤b,…

Q: Minimum distance between the parabolas y² – 4x –8y + 40 = 0 and x² –8x –4y + 40 = 0 is (A) 0 (B) 3…

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Q: 11. Evaluate ([(y+z³ )dS where S is the part of the paraboloid x = 4- y – z² that lies in front of…

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Q: Calculate [ 12/20 ds where C is the parabola r(t) = (t, t², 0). Let 1 ≤ t ≤ 4. X

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Q: Find the minimum of f(x,y) = 5x + 2y on the ellipsoid 9x2 + 2y2 = 7. Leave your answer correct to…

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Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

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Q: Obtain the Solution x, y > 0, xy > 1 of 1 the PDE Ury Such that x+y 2у и 3 0, их on the hyperbola…

A: 1st we set up the initial value condition and draw the figure than set up PDE and solve it

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

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Q: Find the equation of the plane that passes through the point (2, 1,2) and is tangent to the surface…

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Q: Q4/Find the abs.max and abs.min valuse of the huctu f,y) = \+xy-3x on the cosol regen oounded by the…

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Q: Determine the equation of the normal line to the hyperbola x - 4y- = 9 at (5, 2). 8x + 5y – 50 = 0…

A: Given equation of hyperbola is  x2-4y2=9          ...(1) We have to find the equation of the normal…

Q: Q3. Find the point(s) on the surface xyz 1 closest to the origin. %3D

A: Given: To find the points on the surface xyz=1 is given as,

Q: Find the equation of the tangent plane to the surface 9x +36y +4z? = 108 at the point (-2,1,-3).…

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Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: Find the extreme value of the function f(x, y) = xyon the ellipse x2 + 2y2 = 1.

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Q: dy 8) Find for the hyperbola defined by the equation y2 – x2 = 7. dx

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Q: D is the region enclosed by the parabolas z = y²-9 and 2 - y² +9.

A: Let, I=∫∫Dx+y+2dA x=y2-9 and x=-y2+9 Power rule for the integration: ∫xndx=xn+1n+1+C ∫cdx=c∫x0dx=cx

Q: 11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the…

A: We will evaluate the given integral.

Q: Evalute ff Rx²dA, where R is the region in the first quadrant bounded by the hyperbola xy = 16 and…

A: The given integral: ∫∫Rx2dAWhere R is the region in the first quadrant bounded by the hyperbola…

Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

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Q: 5xyz dv, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), and (1, 0,…

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Q: The line x=C where C70 intersects the cubic y= 2x3 + 3x²-9 a七 the point P and parabola y = 4x+ 4x +5…

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Q: Q2) Find the equation of the tangent to the hyperbola x? – 3y² = 1 at the point S(2,-1). %3D A) 2x +…

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Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

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Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

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Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2