Find the equation for the tangent plane and the normal line at the point Po(3,1,3) on the surface x + 3y + 2z² = Using a coefficient of 1 for x, the equation for the tangent plane is Find the equations for the normal line. Let x = 3+ 6t. x=0, y=D z= (Type expressions using t as the variable.)

Q: Q1) Find equations of the Normal plane and Osculating plane of the curve y = 2t, x = 2 sin 3t , z =…

A: We have to find Normal and oscillating plane from given information.

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(6,0,6) on the…

A: Use tangent plane equation

Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

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Q: nd an equation of the tangent plane to the given surface at the specified point. z = 4x² - y² + 4y,…

A: Topic:- application of derivatives

Q: 3. Find the equation of the tangent plane and normal to the surface z =x? +y? + 4 at point (1, -1,…

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Q: Find an equation for the tangent plane and find the parametric equations for the normal line to the…

A: I am attaching image so that you understand each and every step.

Q: 11. Find an equation of the tangent plane to the surface Va+Vy+Vz=4 at the point P(4,1, 1). 12. Find…

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Q: of the tangent plane to the surface z=e-4x/17ln(1y) at the point (-3, 4, 2.808).

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Q: The equation of the tangent plane to the surface x(и, v) %3D (и + v)e, + (и - v)е, — иwe, at X(1,-1)…

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Q: The normal line at point P(0,a,-a) of the surface given by the equation F(x,y,z) = 3xyz – z' – a' =…

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Q: (c) The tangent plane to the graph of z. = f(x, y) at the point (1, 0, 1) can be described by the…

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

A: Solve by using formulas of tangent plane and normal line

Q: Find an equation of the normal plane of the curve at the given point. x=sin(2t), y=-cos(2t), z=4t;…

A: The equation of the normal Plane of x=sin(2t) , y=-2cos(2t) , z=4t ; at point   0,1,2π   is…

Q: Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 6y),…

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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: Determine the slope of the tangent line to the curve of intersection of the surface f(x, y) x + 2y x…

A: According to the guidelines, we are answering first question. Please repost the remaining.…

Q: (a) Find the directional derivative of φ = x2 + sin y −xz in the direction i+ 2j−2k at the point (1,…

A: a) Given that φ=x2+siny-xz Now first evaluate gradient of φ, so…

Q: Find the equations of (1) tangent plane and (2) the normal line to the given surface at the…

A: Equation of tangent plane at x0, y0, z0 is, z-z0=∂z∂xx-x0+∂z∂yy-y0 Equation of a line with normal…

Q: 2. For the function h(x,y) = x³y+ xy2 -x +5 find h and h, and then find the tangent plane to h(x,y)…

A: Tangent plane to the funy h(x,y)

Q: (b) The tangent plane to the graph of z = f (x, y) at the point (1, 0, 1) can be described the…

A: We need to find the tangent plane to the graph of f(x,y)=e3yx4 at the point (1,0,1)

Q: 6. Find an equation of the tangent plane and a set of symmetric equations of the normal line to the…

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Q: Find the equation of the tangent plane to z=e^y+x+x^3+5 at the point (5,0,136)

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Q: The plane y = 1 intersects the surface z = x^4 + 6xy − y^4 in a certain curve. Find the slope of the…

A: The intersection of surface z=x4+6xy-y4 and plane is y=1 is z=x4+6x1-14z=x4+6x-1

Q: Assuming that z is a function of x and y, find the equation of the tangent plane and the equations…

A: Simplify the given equation of the surface to obtain 0 in the right side.…

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

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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: Find an equation of the plane tangent to the following surface at the given point. yz e xZ + 14 = 0;…

A: yzexz+14=0 f=yzexz+14 take partial derivative w.r.t. x fx=∂∂xyzexz+14 fx=∂ ∂ xyzexz+∂ ∂ x14…

Q: ind the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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

A: Equation of tangent plane

Q: Consider the family of curves y I 1+ GI

A: We have y=x1+c1x Differentiate with respect to x: dydx=ddxx1+c1x⇒dydx=1+c1xdxdx-xd1+c1xdx1+c1x2…

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 20, (1, 5, 4) (b)…

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Q: Find the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

Q: Let f (x,y)=x2+5xy−4y2. Then a standard equation for the tangent plane to the graph of f at the…

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Q: a.find the tangent plane to the implicit surface at the point (0, 1, 1) given ye"* + yz² = 2xy³ + 2…

A: We have Fx,y,z=yexz+yz2−2xy3So,the surface implictly is written as Fx,y,z=2Now…

Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1,…

A: We have to solve given Questions.

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 4, (1,2, 9)

A: We know that the equation of tangent plane to the curve z=f(x,y) at point (a,b,c) is

Q: The equations of the tangent plane and of the normal line to the graph of f (x, y) = x-y / x + y at…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 8, 8) 10…

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Q: 1. For the function f(x, y) = In root (2 + xy), find the equation of the tangent plane at the point…

A: Note: As per the guidelines we are supposed to answer only one question because this is not a…

Q: The plane y = 1 intersects the surface z = x4 + 6xy - y4 in a certain curve . Find the slope of the…

A: Given :Plane y=1 intersects the surface…

Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z? = 22, P =…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = 2(x − 1)2 +…

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Q: Find equations for the tangent plane and the normal line at point Po (Xo Yo.Zo) (5,2 on the surface…

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

Q: Q2: Determine the tangent plane and normal line to the surface x^2+2xy-y^2+z^3=7 at point (1,-1,3)

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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

A: The given surface is: f(x,y)=x2-2xy+y2Given point is:  P=(1, 2, 1)

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (5, 3, 16)…

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Q: Find a standard equation for the tangent plane and parametric equations of the normal line at the…

A: Given surface is xlny+ylnz=x

Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

A: Let the equation of the surface be, fx,y,z=x2-xyz-165 Consider that fx, fy, and fz denote the…

Q: 1. Find the equation of the tangent plane to the surface by rly.v)- cu', vuu+ 2v > at the point (1,…

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