f(T, y) = V 35x + 2y Find the slope of the surface z = f(x,y) in the y-direction at the point (4, 2).

Q: The equation of tangent plane to the surface f(x, y, z) = x² + y? +z-9 = 0 at the point (1,2, 4) is…

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Q: Find an equation for the plane that is tangent to the surface z=ln(x2+y) at the point P(0,1,0).

A: we have to find the equation of the tangent plane

Q: The slope of the surface z = xy² in the x-direction at the point (2, 3) is _____, and the slope of…

A: Given:z=xy2   x-directionat the point 2, 3 y-directionat the point 2,3

Q: Let f(x,y) = xe-Y + 5y. a) Compute fr and fy. b) Find the slope of the surface z = (2, 5). f(x, y)…

A: We have a function fx,y=xe-y+5y. We have to answer the following...

Q: Find the equation of the tangent plane to the surface 4xe^yz+xz^2−7x^3y= 5 at(1,0,1).

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Q: The equation of tangent plane to the surface f(x,y, z) x+ y +z-9 0 at the point (1,2,4) is x+y+z=…

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Q: Find the equation of the plane tangent to the surface G(x,y, z) = 2x² - y² – 3z2 = -4 at P = (-2,…

A: Given surface is                                                G(x, y, z): 2x2-y2-3z2=-4 we have to…

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: Find the general equation of the tangent plane to the surface x2 + y2 −2xy −x + 3yz = −4 at the…

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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 an equation for the tangent plane to the surface z = 6x3y2 + 3y at the point P(1, -3). Hint:…

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Q: Find the equation for the tangent plane to the surface Z =-8x² - 3y2 at the point (2 1, -35). O 2x +…

A: We can find the answer as below

Q: 7. Find the equation of the tangent plane to the surface: x² + y* -z =i, at (2, 1,2)

A: Given : x2+y2-z2=12z

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

A:

Q: Given the surface z = In(-2x² + 5y² – xy). Find the directional derivative of the function f at…

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Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

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Q: If f(x, y, z) = V3x + y² – 2z, then find the slope of the surface f in the r- direction at the point…

A: Final answer is 3/2

Q: Q2: A. For the surface f derivative at (1,1 derivative and the line to the surface

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Q: Q4) given the surface: cos nx – x²y + exz + 2yz = 2 Find the equation of the tangent plane and…

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Q: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

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Q: 9) Find a point on the surface z = 8- 3x2 - 2y2 at which the tangent plane is perpendicular to the…

A: In this question we have to find a point on the surface at which the tangent is perpendicular to the…

Q: Find an equation for the plane tangent to the surface e z = x cos(xz) – y at the point (2, 1,0).

A:

Q: For the surface f(x,y, z) 2*y, find: The gradient of the surface at the point (1,2,1);

A: Gradient of a function

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: The equation z = f(x,y) = y +x -3y defines a surface. What is t- equation of the tangent plane at…

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Q: Find the equation oftangent plane and normal lines ofthe surface: f(x,y, z) = 10x² –14 y² +11z³-7 at…

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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: Find an equation of the tangent plane to the surface x2 + 2y? + 3z2 = 6 at the point (1, 1, 1). O A.…

A: As we know that the equation of the tangent plane: nxx-x0+nyy-y0+nzz-z0=0 Given:…

Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

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Q: Given a surface f(x,y) = -2x² + (5)y². Find the derivative in the direction of v = at the point (7,…

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Q: The equation of the tangent plane to the surface X +y- z = (2, –1, -1) is 2 at the point | O a) None…

A: This question can be solved by applying the formula of equation of tangent plane to the given…

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: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

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Q: Find the equation of tangent plane to the surface x^2 + 2y^2 + 3z^2 = 21 which is parallel to the…

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Q: Find the point on the surface f(x,y)=x+y2+xy-24x+2y at which the tangent plane is horizontal.

A: We have to find the points for horizontal tangent plane.     According to our guidelines , We can…

Q: Find an equation of the plane tangent to the surface xy z2 = 2 at the point (2, 1, -1). %3D

A: Given that XY3 Z2 =2 And point (2, 1,-1).

Q: Find an equation of the tangent plane to the surface f(x, y, z) = x 2 + y 2 + xy − yz − xz + z 2 − 2…

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Q: Find the equation of tangent plane to the surface x² + 2y? + 3z2 = 21 which is parallel to the plane…

A: Topic- equation of tangent to surface

Q: Find the equation for the tangent plane and the normal line at the point Po(2,3,1) on the surface 3x…

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Q: Let ƒ(x, y) = x2 + y3. Find the slope of the line tangent to this surface at the point (-1, 1) and…

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Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

Q: Find an equation for the plane tangent to the surface e'z = x cos(xz) – y at the point (2, 1, 0).

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Q: Find an equation of the tangent plane to the surface x-xyz 56 at the point (-4,5,2). Select one:…

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Q: Find an equation for the tangent plane to the surface given by f(x,y)=÷(4x² – 2y²) at the point…

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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 slopes of the surface in the x- and y-directions at the given point.

A: It is given that,z=xy  and point (1,2,2). We have to find the slopes of the surface in the x- and…

Q: Find the equation of tangent plane to the surface x? + 2y? + 3z2 = 21 which is parallel to the plane…

A: equation of the tangent surface of  F= x2+ 2y2+ 3z2= 21   which is also parallel to the plane…

Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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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.