Let z=f(x,y) = y² – x³ . Find the slope of the line tangent to this surface at the point (-1, -2) and lying in the a) plane x= -1 b) plane y= -2.

Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: (b) Compute the slope of the line that is parallel to the xz-plane and tangent to the surface z = x…

A: Given: Let's calculate the slope of the line tangent to the surface z=x(x+y) at the point that is…

Q: Find the 'slope' of the tangent line to the curve of intersection of this surface 3z = 36-9x –4y?…

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Q: Find an equation of the tangent plane to the surface xyz = 10, at the given point (1, 2, 5), and…

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Q: Find a point on the ellipsoid x + 3y² + z = 8 where the tangent plane is perpendicular to the line…

A: Introduction: The perpendicular vector to a 3D object f ( x, y, z ) can be calculated by computing…

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A: Here we have to find the equation of rectifying plane to We have,

Q: Identify all points in which tangent plane to z=f(x,y)= x2+y2 is perpendicular to the x-y plane.

A: Given:-                                      Identify all points in which tangent plane to…

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

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Q: Find the plane tangent to f(x,y)=x/(x+y) at the point (1,5).

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Q: Find the equation of the tangent plane to the surface defined by the function f(x, y) = x³…

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Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

Q: Determine equation of tnagent line to the common curve of 2 surfaces w/ equations: z = x? + y – 2xy…

A: follow next step

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the slope of the tangent in the positive y-direction to the surface  z = 3x + 2y − 4exy at (4,…

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Q: Let F(x, y, z) =7x2+8y2+13z2. Find the equation to the tangent plane to the level of surface F(x,…

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Q: Find an equation of the tangent plane to the surface x = u² + 1, y = v³ + 1, z = u + v at the point…

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Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

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Q: Find the equation of the tangent plane to the surface z = 4 号+ゾ + y² at the point (2, -3, 10)

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Q: Find equations for the tangent plane and the normal line at point Po (X0,Yo,Zo)(1,5,0) on the…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given point (2, 2, 8)…

A: To Determine: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given…

Q: Find the angle of inclination of the tangent plane to the surface x2+ y2+ z2 = 14 at the given point…

A: Consider the function fx,y,z=x2+y2+z2-14. Gradient of f can be obtained as follows. ∇fx,y,z=∂∂x,…

Q: Find an equation of the plane tangent to the surface sin(xyz) = at the point (T, 1,-)

A: sinxyz=12 at the point π, 1, 16. Consider, sinxyz=12⇒xyz=sin-112⇒xyz=π6⇒z=π6xy Differentiating…

Q: Find the point(s) on the surface at which the tangent plane is horizontal. z = 9 - x2 - y? + 4y (х,…

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Q: Find the equation of the tangent plane to the surface determined by x*y + z – 35 = 0 at x = 3, y =…

A: Given x4y4+z-35=0

Q: Find an equation of the tangent plane to the surface z = In(x - 2y) at the point (3, 1,0) %3D

A: Given that, z = ln (x - 2y) we have to find the equation of tangant at point (3, 1, 0).

Q: Find an equation of the tangent plane to the surface zx + 2xy + 3yz3 = 6 at a point in the…

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Q: Find the equation of tangent plane and normal lines of the surface: f(x, y, z) = 5x² + 4 y2 +z³-9 at…

A: Here we have to find the equation of the tangent plane and normal lines of the surface:…

Q: Find the equation of tangent plane and normal lines of the surface: ( x, y, z) = 5x^2 +  4y^2 + z^3…

A: We have to find the equation of tangent plane and normal lines of the surface: f(x,y,z)=5x2+…

Q: Let f(x,y)= e, Compute the cartesian equation of the tangent plane r,y) at the point (2.2).

A: The equation of tangent plane

Q: Find the equation of the plane tangent Z = (x+2)*- (y-1)²-5 at (2,3,3) to

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Q: Find an equation for the tangent plane to the surface x = u² – v², y = u + v, 2 = u² + 4v at (-},2).

A: We have r(u,v) = (u2-v2)i + (u+v)j + (u2+4v)k

Q: Let C be the curve on the xy-plane that is the projection of a horizontal cross-section of the…

A: Given surface is,yz=ln(x+z) zxy=1x+z(1+zx)y-1x+zzx=1x+zzx=1y(x+z)-1 Take the derivative with respect…

Q: Find the equation of the tangent plane to the surface f(x,y)=In(4x²-2xy-y²) at the point P(-1,-1,0).

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Q: Find the slope of the tangent in the positive y-direction to the surface z = 3x + 2y − 5exy at (3,…

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Q: Find the equation of the tangent plane and normal line to the surface at the given point. x2 z = 9…

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Q: find an equation for the plane tangent to thesurface z = ƒ(x, y) at the given point. z = 1/ (x2 +…

A: Concept - Equation of plane is given by - Ax-x0+By-y0+Cz-z0 = 0         ...............(1)where,x0,…

Q: Find the equation of the plane tangent Z= x2+ Y2 at point P (1,2,5) to the surface

A: Equation of tangent plane on the surface z=f(x,y)  at the point (a,b,c)  is given…

Q: Let C be the curve on the xy-plane that is the projection of a horizontal cross-section of the…

A: Given that,

Q: Let ƒ(x, y) = 2x + 3y - 4. Find the slope of the line tangent to this surface at the point (2, -1)…

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Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

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Q: Find the distance between the plane x+y +z = 3 and the line L= λ(1,0,-1).

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Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

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Q: Compute the equation of the tangent plane to the surface: y = 1 - x2 - 2z2 At the point (0, 1, 0)

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Q: Find the angle of inclination of the tangent plane to the surface 3x2 + 2y2 − z = 15, at the given…

A: We have given surface 3x2+2y2-z=15 at point (2, 2, 5)   We have to find the angle of inclination…

Q: Let f(x.y) = x° +y*. Find the slope of the line tangent to this surface at the point (- 1, - 1) and…

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Q: Find the equation of the tangent plane to the surface y = 2x² – z² at the point (0,-1, 1)

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Q: Find an equation of the tangent plane to the surface z = √(9 − x2 − y2), at the given point (1, 2,…

A: The surface given is Fx,y,z=√(9 -x2 -y2) -z =0. The derivative of the surface coordinates with…

Q: Let z=f(x,y) = y x². Find the slope of the line tangent to this surface at the point (-2, -1) and…

A: 5.

Q: Determine the equation of the tangent plane and normal line to the surface at the given point.…

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