Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x – 4y – 3 -

Q: If E is the solid that lies under the plane z = 3 which its base on the xy-plane is between the two…

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Q: Find the plane tangent to the surface z=x x+ y° at the point (3,4,25). a. 6x+8y-z=25 O b. 6x-8y-z=25…

A: As we know that; The equation of the tangent plane: nxx-x0+nyy-y0+nzz-z0=0 And The normal vector at…

Q: Find an equation of the tangent plane to the given surface at specified point. a) z = e*y +…

A: Here To find the equation of the tangent plane to the given surface at specified points,  we will…

Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

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Q: An equation of the tangent plane to the surface z = 4xy² + 3x²y² at the point (1, 1, 7) is: Select…

A: z= 4xy2+3x2y2F(x,y,z) =…

Q: Find the coordinates of the centroid of the curvex = et cos t, y = et sin t, 0 ≤ t ≤ p.

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Q: Find the tangent plane of the surface z = f(x, y) at (0,0, 0) in which 3y f(2, y) = || cos /3 t dt.

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Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: Consider x=h(y,z) as a parametrized surface in the natural way. Write the equation of the tangent…

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Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: Find the equation of the tangent plane to *+ y? at the point (2, –3, 10) the surface z = 4 O x + 4y…

A: We have to find

Q: Let (S) be the surface given by the following equation. x²+y² = 1+ z?. An equation of the tangent…

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Q: Find the parametrization r(t) = [x(t), y(t), z(t)] of the curve obtained by intersecting the…

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Q: Give the integral representing the length of the parametric curve x=t^3, y=t^4, 0≤t≤1.

A: Given: A parametric curve:   Now the length of the parametric curve is given by the formula:

Q: Let F(x, y, z) = 15x? + 12y2 + 10z?. Find the equation to the tangent plane to the level of surface…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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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: Consider x = h(y, z) as a parametrized surface in the natural way. Write the equation of the tangent…

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Q: a) Find the points at which the twisted cubic F(t) = ti + t} +tk intersects the plane 4.x +2y+z = 24…

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Q: (a) 'Find the orthogonal trajectories on the surface of the sphere x' + y? + z = 0 with the…

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Q: H.W: find the tangent plane to the surface z = Vy -x at the point (1,2,1)

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Q: The equation of the tangent plane to the surface yey +z =0 at the point (0,-1,1) is az+by+cz = 1.…

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Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

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: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

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Q: Find an equation of the plane tangent to the following surface at the given points. z= eW; (4,0,1)…

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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: 2. Let z = f(x,y) = x³ + xe* +y?. (a) Find an equation of the tangent plane to the surface z = f(r,…

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Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

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Q: . Show that the tangent plane to the surface 2yyo cz at the point P(xo,Y0, zo) is given by the 2rro…

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Q: The slope of the tangent line to the curve of intersection of the plane x = xo and the surface z =…

A: Proceed as shown below

Q: Calculate the positive value of m so that the x+y+2z=m plane is tangent to the spherical surface…

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

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Q: Find the equation of the tangent plane Pr to the surface S:r + y? + z? = 9 at (2, 1, –2) O Pr: 4x –…

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Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface…

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Q: Find a parametrization for the curve that matches the lower side of the parabola x-1=y2. A. x =…

A: Solution:

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

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Q: If the tangent plane to the surface z = +y is parallel to the plane r+ 2y-z 0 at the point (1, a,…

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Q: At what points does the curve r(t) = ti + (6t – t2)k intersect the paraboloid z = x² + y2? (If an…

A: Given, r(t)=t i +(6t - t2)k ......(1) and z=x2+y2 .......(2)

Q: Find an equation for the tangent plane to the surface z = 3y^2 − 2x^2 + x at P(2, −1, −3). Express…

A: Let's find equation of tangent plane.

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: Show that the curve r(t) = (ln t)i + (t ln t)j + t k is tangent to the surface xz2 - yz + cos xy = 1…

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Q: Show that the tangent plane to the surface x 2 a 2 + y 2 b 2 = cz at the point P(x0, y0, z0) is…

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Q: Evaluate the unoriented line integral +y² + z²) ds along the parametric curve a : [0, 1] → R³ with…

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Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

A: First we have to find partial differentiation with respect to x , y and z of function f such that-

Q: Which of the following is the equation of the tangent plane to the surface z=x2 - x+3y² +y at the…

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Q: Find the equation of the tangent plane Pr to the surface S:r +y +z2 = 9 at (2,-1, 2) | O PT:4x + 2y…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: Use Stoke’s Theorem to evaluate the line integral ∮C(z2−y2)dx +(x2−z2)dy +(y2−x2)dz, where the curve…

A: Given equation of the curve is ∮C(z2-y2)dx+x2-z2dy+(y2-x2)dz ,the equation of the paraboloid…