Given a surface, ƒ(x,y,z)=15, explain what you would do to find the equation of the tangent plane at a point on the surface, P. Be clear about what you would do, in what order and why you would be doing what you say.

Q: Find the equation of the tangent plane Pr to the surface S: x2 + y? +z² = 9 at (2, –1, 2)

A: The equation of the tangent plane to the surface f(x, y, z)=0 at a, b, c is defined as: fxa, b,…

Q: Find an equation for the plane tangent to the given surface at the specified point. z = v², y = u? +…

A: Given that

Q: 3. cos Tx – x*y + e*z + yz = 4 at point Po(0, 1, 2). -

A: The given surface at the point P0 is    Cos(pix) - x2y +exz + yz = 4

Q: Find the equation of the tangent plane to the given surface at the specified point. z=xsin(x+y),…

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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 an equation of the plane tangent to the following surface at the given points. zexy; (1,0,1)…

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Q: Under what conditions can you find the area of the surface generated by revolving a curve x = ƒ(t),…

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Q: find an equation for the plane that is tangent tothe given surface at the given point. z = ln (x2 +…

A: The given function is It can be written as as the given function has both variables x and y.

Q: Given the surface x²y + y° z+ z?x = 38. Find the normal line and the tangent plane to the given…

A: A detailed solution is given below.

Q: Find an equation of the tangent plane to the surface defined by the equation zf(x, y) + 2³ = 3 at…

A: The given surface is:zf(x, y)+z3=3The point is (-1, 2, 3)

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = √(y - x),…

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Q: Find all points on the surface given below where the tangent plane is horizontal. 2 Z=X ? - 3xy-y -…

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Q: z = In (x² + y²) at point Po(1,0, 0).

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Q: The horizontal tangent plane of the surface z = 4x – xy – 2y – 2x – 8y – 3 is given by the equation…

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Q: Find the point(s) on the surface z = 5xy, at which the tangent plane is horizontal.

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Q: 2. For the surface z = In(y+ Vx² + y²). (a) Find an equation of the tangent plane at the point (3,…

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Q: Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in…

A: Let's find.

Q: At which of the points below is the tangent plane to the surface x² – 2y + z + yz = 2 vertical?…

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Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

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Q: Find an equation of the tangent plane to the surface z = 2a2 + 1y – la – 3y – 1 at the point (5, 3,…

A: Equation of Tangent Plane to the surface F(x, y, z) = 0 at point (x0, y0, z0) is given by ∇F(x0, y0,…

Q: (b) Find the point that makes the tangent plane to the surface z = x² – xy + y? – 2x + 4y…

A: Find the partial derivatives with respect to x and y and set equal to zero. Solve for x in the…

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

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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: Consider the level surface 3x?y + 14z° = 3, the angle in degrees that the z-axis makes with the…

A: The given level surface: The angle in degrees that the z-axis makes with the tangent plane at point…

Q: If the curve y = f(x), a ≤ x ≤ b, is rotated about the horizontal line y = c, where f(x) ≤ c, find a…

A: Given, Curve y= f(x) , a≤x≤b Rotated about a horizontal line y=cwheref(x)≤c

Q: Find the area of the surface obtained by rotating the curve y 4V7,0 < I < 5, along the r-axis.

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Q: Find the equation of the tangent plane to the surface determined by z'y' + z – 25 = 0 at z = 4, y =…

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Q: 3. z = (c

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Q: Find the point on the surface f(x,y)=x2+y2+xy-26x+29y at which the tangent plane is horizontal.

A: For Given surface f(x,y) The slope of horizontal tangent plane is equal to zero.

Q: Find all points on the surface given below where the tangent plane is horizontal. z = 5x - 6xy - 5y…

A: We know the slope of the horizontal tangent plane is zero. So we can put ∂z∂x=0 and ∂z∂y=0.

Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

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Q: The area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: Area of ellipse initially  = Ai  = πab    Now, lengths of axis are changed,   They are  [ 2(1.0099)a…

Q: Find the tangent plane to the surface z = 9 – x* – y? at the point (1, -3, –1).

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Q: Find the tangent plane to the surface given by the following pa the point (8,14.2). F (u,v) = (n² +…

A: Solution:- The tangent vectors are:- ru=&lt;2u+2,-2,0&gt;rv=&lt;0,3,6&gt; ruxrv=ijk2u+2-20036…

Q: Find the equation of the tangent plane Pr to the surface S:x2 +y? + z2 = 9 at (2,-1, 2)

A: To find :Equation of tangent plane to the surface x2+y2+z2=9 at the point (2,-1,2).

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: Let C be the curve y =x3/2, 1 < x < 4. (a) Find the length of this curve. (b) Find the surface area…

A: Given curve is

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 11x ,(z = 0)…

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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 standard form for the TANGENT PLANE to the surface: : = f (x,y) = x cos (xy) at the point…

A: The given function is  z = f(x,y) =x cos(xy)

Q: (b) Find the point that makes the tangent plane to the surface z = x- xy +y-2x + 4y horizontal.

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

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Q: Given a surface, f(x,y,z)=15, explain what you would do to find the equation of the tangent plane at…

A: Procedure to find tangent plane at a point on the surface:

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x (1, 9, 9) %3D…

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Q: Find the equation of the tangent plane to the surface determined by a'y + z- 55 = 0 at a = 4, y = 3.…

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Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: The area of the surface obtained by rotating the curve * = 3t, y = 67 – 4t 5 st s 6. about x-axis is…

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Q: Find the equation of the tangent plane to the surface z = +y? at the point (2, –2, 5)

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