29. Find parametric equations for the tangent line to the cur ve of intersection of the paraboloid z = x² + y² and the ellipsoid x² + 4y? + z? 9 at the point (1, –1, 2). %3D

Q: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

A:

Q: EXAMPLE 9 Find the tangent plane to the surface with parametric equations x = u2, y = v2, z = u + 2v…

A: Given parametric equation x=u2 , y=v2 , z=u+2v

Q: 1. Consider the ellipsoid x² + y² + 4z? = 12. (a) Find an equation of the tangent plane to the…

A: As per bartleby guideline for more than one question, only 1st one is to be answered. Please upload…

Q: 1. Find all points Po on the ellipsoid 2x2 + 3y? + 2z2 plane x – 3y + 2z = 5. = 22 at which the…

A: To find points P0 on the ellipsoid 2x2+3y2+2z2=22   The tangent plane is parallel to the plane…

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: Find a point on the hyperboloid x2 + 4y2 – z2 = 1 where the tangent plane is parallel to the plane x…

A: Given  and plane

Q: Find the radius of curvature at 0 = t of the parametric equations x = 3(0 + cos 0), y = 3(1 – cos…

A: To find the radius of curvature, first find out dxdθ and d2xdθ2. x=3θ+cos θdxdθ=31-sin θd2xdθ2=-3cos…

Q: Sketch the surfaces CYLINDERS z = y2 - 1

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

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

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Q: 15. Find the radius of curvature at 0 = -n of the parametric equations x = 3(0 + cos 0), y = 3(1 –…

A: For the parametric curve x=x(θ), y=y(θ)Curvature K=|x'y''-y'x''|[(x')2+(y')2]32Radius of…

Q: Find the extreme values of ƒ(x, y, z) = x( y + z) on the curve of intersection of the right circular…

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Q: 15. Find the radius of curvature at 0 = ÷n of the parametric equations x = 3(0 + cos 0), y = 3(1 —…

A: Given two parametric equations, x=3(θ+cosθ),y=3(1-cosθ) To find the radius of curvature at θ=π3

Q: (7.5.0)- Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point %3D

A: Given F(x, y, z)=z-sin(x-2y) ∂∂xF(x, y, z)=∂∂x(z-sin(x-2y))=-cos(x-2y)∂∂yF(x, y,…

Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…

A: Radius =6  r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k

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: 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: 6. What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z…

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Q: 2. Bounded by the paraboloid = 10 – 322 – 3y? and the plane z = 4 (using polar coordinates)

A: The paraboloid is bounded by z=10-3x2-3y2 . Now, converting in polar coordinates, z=10-3r2.

Q: Determine the total distance covered from t = 1 to t = 3 from the given parametric equations: x =…

A: Let's find the total distance covered. = d

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: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: 1. Find the closest point of the surface ry + xz + yz = 1 to the origin. %3D

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Q: 3. Find an equation of the tangent plane to the paraboloid defined by z= 5x +4y? at the point…

A: The given equation is; z=5x2+4y2 at the point (-1,1,9).

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x2 + y? + 22…

A: Solution :-

Q: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

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Q: B.2. Express to its standard form, determine the center, radius ar 10. x² + y? + 10x – 14y + 58 = 0…

A: # We are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…

A: We have to find the equation of the tangent plane to the hyperboloid x² + 3y² − 3z² = 1 at the point…

Q: Are there any points on the hyperboloid x 2 − y 2 − z 2 = 1 where the tangent plane is parallel to…

A:

Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

A:

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: 3. Find the exact area of the surface obtained by rotating the curve described by the parametric…

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Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x²…

A: Given :-  The curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid x2 + y2 + z2 =6…

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

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Q: 14. Under the paraboloid z=x² +y2 and above the disk x +y² <9 for (x,y) in the first quadrant.

A: we have to find the volume

Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Use definition 13.7.1 to find the equation of the tangent plane and the parametric equations for the…

A: Let the given function is,

Q: Let C be the curve of intersection of the parabolic cylinder x = 2y, and the surface 3z = xy. Find…

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Q: Find an equation of the plane tangent to the following surface at the given points. z =6 cos (x- y)+…

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Q: Let C be the curve of intersection of the spheres x 2 + y 2 + z2 = 3 and(x - 2)2 + (y - 2)2 + z2 =…

A: Let fx=x2+y2+z2-3=0 &amp; gx=x-22+y-22+z2-3=0 At P=(1, 1, 1) ∇f=2x, 2y, 2z∇fP1, 1, 1=2, 2, 2…

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + Z?…

A: Solution-

Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

A:

Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

Q: Find the equation of the tangent plane to the surface 3D1 16 at the point (1,-3,2) O a. 2x+4y-3z=12…

A:

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: Are there any points on the hyperboloid x² – y² – 2² = 1 where the tangent plane is parallel to the…

A: By see this solution

Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

Q: 12. Let H be the hyperboloid where x² – y² + z² = 6. Find an equation for the tangent plane to H at…

A: As you asked only solution for Q12 so, I answered here only Q12

Q: Find the equation of the tangent plane to the surface z =e/ In (2y) at the point (2, 4,1.643). Note:…

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Q: Are there any points on the hyperboloid r² – y² – 2² =1 where the tangent plane is parallel to the…

A:

Q: 14. Find a point on the surface z = 3x- y at which the tangent plane is parallel to the plane 6x +…

A: