(4) The equation of the tangent plane to the surface In = z²(x – 2y) + 3z +3 at (4, 2, –1) is 2y

Q: Find the point where the tangent line to the curve 7(?) = (V? +3,ln(?² +3),t) at (2, In 4,1) 5. %3D…

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Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

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Q: The number of antelope in a national park is modeled by the function dA A that satisfies the…

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

Q: An equation of the tangent plane to the surface z = 2 y? - x² at the point (2,-2,4) is: (A) 4 (x –…

A: z=f(x,y)Let F(x,y,z) =f(x,y)-zEquation of tangent plane is given by,    Fxxo,yo,zo(x-xo) +…

Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

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Q: Find an equation of the plane tangent to the surface z = x2 + y2 at (2, 3, 13). [Hint: Consider the…

A: Note: Here, f(x,y,z) = x2 + y2 - z and the point is (2, 3, 13).

Q: )8 درجة( 1(ليكن لدينا المصفوفات التالية: 1 5 2] -1 0 1 2 4] 01 A =|-1 2 3 D = ; - [1 4 21 •B = [3 l3…

A: Multipart :   We have ,  A = 30-1211 , B = 142315 , C = 152-101324 , D = 3-10-2 (a) We need to find…

Q: Find an equation for the tangent plane to the surface 2³-xy¹ = 0 at the point (1,3,1). 81

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Q: The equation of the tangent plane to the surface ye+z 0 at the point (0,-1,1) is az+by+cz 1. Which…

A: If  F(x, y,z)=0 is a three variable real valued function and generates the surface S, then the…

Q: Find the equation w=T(x,y,z) of the tangent hyperplane at p. F(x,y,z)=3x²-2y²+xz², p=(1,2,-1)

A: General equation for the tangent to the plane is expressed as:…