Let C be the curve on the xy-plane that is the projection of a horizontal cross-section of the surface yz = In(x + z) and that passes through the point (–1,0). Then the tangent line to 6 at (-1,0) is represented by the equation x x+ x y = 1.

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

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Q: Find the slope of the tangent line to the curve that is the intersection of the surface z = x2 - y2…

A: Calculate point of intersection and differentiate it to get the answer

Q: Find the equation of the tangent plane to the surface z=9x^5+2y^5+1xy at the point (0,−1,−2) z=

A: From tangent plane equation to a curve

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 the equation of a tangent plane to the surface of z = eª cos(y) at the point P(0,0, 1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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: Find the point(s) on the surface z = x2 − xy + y2 − 2x − 2y, at which the tangent plane is…

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Q: find the tangent plane to the surface z = y-x at the point (1,2,1)

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Q: Find an equation for the tangent plane to the surface z + 1 = xy² cos(z) at the point (1, 1, 0)

A: The given equation is z+1=xy2cosz. The objective is to find an equation for the tangent plane to the…

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

A: Given,

Q: 1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).

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Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 3 at the given point( 2, 1, 8).

A: Known fact: Let F(x,y,z) be the surface which is differentiable at P(x0, y0, z0). then the equation…

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 the equation of the tangent plane to the surface z = ln (2x + y) at the point (-1,3,0) .…

A: To find the equation of the tangent plane to the surface z=ln2x+y at the point -1, 3, 0.

Q: Find an equation of the tangent plane to the surface z=−2x^2+3y^2−x+3y+1 at the point (1, 1, 4)…

A: We have to find the  equation of tangent plane

Q: Find the slope of the tangent line to the curve of intersection of the surface z = x + y' with the…

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Q: Find an equation of the tangent plane to the surface z = 2x² + 1y² + læ + ly – 2 at the point (2, 5,…

A: This question is based on 3d geometry.

Q: Find an equation for the tangent plane to the surface z + 5 = xy° cos(z) at the point (5, 1, 0).

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y2,…

A: This question is based on finding equation of tangent plane.

Q: Find the plane tangent to the given surfaces at the specific point f(x, y) = x2 ln(2x+y) in (-1, 3)

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Q: Find an equation of the tangent plane to the surface z= z + 2y² at the point P(1, 1, 3). Nind th…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: 4. Let f(x, y) = sin(x²y) + vx + e+y. Find the equation of the tangent plane to the surface z f(x,…

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Q: Find an equation of the tangent plane to the surface at the given point. 6. f(x,y) = x² – 2xy + y²,…

A: fx, y=x2-2xy+y2,    1, 2, 1. Partially differentiating with respect to x, we get fxx,…

Q: Find the equation for the tangent plane to the surface z = Vy -x at the point (2,3,1). Use a…

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Q: Find an equation of the tangent plane to the given surface at the specified point z = √√√xy, (3, 3,…

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

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Q: Find an equation of the tangent plane to the given surface at the specified point. z2 = x2 + y?,…

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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),…

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

Q: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

A: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

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 the equation for the tangent plane to the surface z = x2 at the point P (1,1,1). Select the…

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Q: 3. Find an equation of the tangent plane to the surface z = 2xy + 4y xy-2x at the point (1,1,-6)

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = y In(x), (1,…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

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

Q: Find the slope of the tangent line to the curve that is the intersection of the surface z=x² - y…

A: The details solution is given below

Q: Find the equation of the tangent plane to the surface z = xy at the point (1, 2, 2) and to the…

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Q: Find an equation of the tangent plane to the surface z = xy at (1,2,2).

A: The given surface can be written as F(x, y, z)=0, where F(x, y, z)=xy-z

Q: Find the equation of the tangent plane to the surface z = 3 e^(x−y) at the point (4, 4, 3)

A: We find the equation of the tangent plane to the surface z = 3ex-y at the point (4, 4, 3).

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: 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

Q: Find an equation of the tangent plane to the given surface at the specified point. z = V xy, (2, 2,…

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