3: For the surface f(x,y, z) = tan(xy + xz + yz), find: (1) the gradient of f; (2) the directional đerivative %3D at (0,1,0) in the direction of ü = i- 2j +2k; (3) the max. and min. directional derivative and their directions; (4) the parametric equation of the tangent plane and the normal line to the surface at (0,1,0). 2,2

Q: Find the equation of the tangent plane (in the form z = ax + by +c where a, b, c are constants) to…

A: Here we use the formula of  ∂f∂x(a,b)(x-a)+∂f∂y(a,b)(y-b)=0 tangent plane to the surface at a point…

Q: Find the parametric equations of normal line to the surface given by f(x,y) = tan Vx2 + y² at the…

A:

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 horizontal tangent plane of the surface z = 2x² – xy – y² + 6x – 6y – 2 is given by the equation…

A: Consider the given equation. z=2x2-xy-y2+6x-6y-2 Find the derivative with respect to x and y.…

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 an equation of the tangent plane to the given surface at the specified point. z = y cos(x - y),…

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Q: An equation for the tangent plane to the surface : = (xty at the point P(1, 1, 4) is a) 8x + 8y -: =…

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

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 an equation of the tangent plane to the surface f(x, y) = x2y at the given point (2, 1, 4) and…

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

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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 an equation of the tangent plane to the given surface at the specified point. z = x sin(y – x),…

A: From the given equation: z=xsin(y-x) And Px,y,z=8,8,0 Let, f(x,y,z)=z-xsiny-x As we know that, The…

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: Find parametric equations for the normal line to the surface z=e2x< + 9y< at the point (0,0, 1). O x…

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Q: If the gradient of f is Vƒ = z j - yi – 2xzk and the poi f(x, y, z) = 0, find an equation for the…

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Q: Find the equation for the tangent plane to the surface x- 5xyz+ y = - 7z at the point (- 1, -1, -…

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Q: Find the equation for the tangent plane to the surface x-9xyz +y= - 11z at the point (-1,-1,-1). O…

A: The given surface is x2-9xyz+y2=-11z2 and the point is -1,-1,-1.

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

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Q: Q3: For the surface f(x, y, z) = tan(xy + xz + yz), find: (1) the gradient of f; (2) the directional…

A: Given

Q: Q3: For the surface f (x, y, z) = tan(xy + xz + yz), find: (1) the gradient of f; (2) the…

A: As per the company's guidelines we are supposed to solve first three sub-parts for you, kindly…

Q: The equation of the tangent plane to the surface f (x,y,z)= xe" cosz- z-1= 0 at the point…

A: Given surface is xeycosz-z-1=0 and the point is A1,0,0 find the equation of tangent

Q: Let h(x, y) = xye-(x²+y²). Classify all local extrema of the surface using the second derivative…

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Q: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: An equation for the tangent plane to the surface (xty at the point P(1, 1, 4) is a) 8r + 8y-:= 0 b)…

A: The given surface is  f(x,y)=z=(x2+y2)2  ...........(1); we have to find the tangent plane at point…

Q: Find parametric equations for the normal line to the surface x2 + 9xyz + y² = 11z2 at the point (1,…

A: Given:- x2+9xyz+y2 =11z2  To find:- Equation of normal line to the given surface at point (1,1,1)

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2…

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

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Q: Find the plane tangent to the surface z = x cos y - yex at (0, 0, 0).

A: Consider the following function: z=fx,y=xcosy-yex Differentiate function fx,y with respect to x:…

Q: Find the point (x, y, z) on the surface z = 2x2 - y where the tangent plane is parallel to the plane…

A: We have to find the point (x, y, z) on the surface z = 2x^2 - y^2 where the tangent plane is…

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: Consider the equation of the surface S given by: exyz + x3z3 − 3y4 = 9 An equation for the plane…

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Q: Let f(x,y)=x*e^(xy). Find the equation of the tangent plane to the surface z=f(x,y) at (1,0,1).

A: Formula:

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

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

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 an equation of the tangent plane to the surface given implicitly by z= sin(zy) at the point (,…

A: A tangent plane to a surface is a plane that just touches the surface at a single point. The…

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: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

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Q: 7. Find an equation of the tangent plane to the given surface at the specified point. cos(x –…

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Q: Find an equation of the plane tangent to the following surface at the given points. z= e*y; (6,0,1)…

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Q: 1) Let h(x, y) = x* – 4xy² – 2x² + 8y². Find and classify all local extrema of the surface using the…

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Q: E For the surface f(x,y, z) = tan(xy + %3D at (0,1,0) in the direction of ü = i- 2j +2k; (3) the…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 3. Consider the surface sin (xy)+ cos (xz)+sin ( yz) =1. Find an equation for the tangent plane to…

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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: 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: 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: Find the equation of the tangent plane to the surface y = 2x2 (0, –1, 2) z at the point O y+ 4z = 7…

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Q: Solve for an equation of tangent plane and parametric and equations of normal line to the given…

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Q: Find an equation of the tangent plane to the surface x2 + y2 + z2 = 9 at the given point (1, 2, 2)…

A: Given equation: x2+y2+z2=9 Consider the given equation, fx,y,z=x2+y2+z2-9=0