1. Fad the equation of the tangent plane and normal line to the surface z = 2r+y at the point (1,1,3). 2. Find the absolute maximum and minimum values of the function [(u.v) =wv² on the set D = ((u, v) : u 2 0, v 2 0, u? +v <3}.

Q: An equation of the tangent plane to the surface 1+y z = at the point p(1, 3, 2) is 1+x (A) (x-1) -…

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

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Q: 3. (a) Show that the two surfaces S1 : z = xy and S2 : z =3x^2/4 - y^2 perpendicularly at the point…

A: As per our guideline, we are supposed to solve only first subpart. Kindly repost other subpart as…

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: In Exercises 1–5, find equations for the (a) tangent plane and (b) normal line at the point P0 on…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: At what points does the curve r(t)=(t,t,14t) intersect the surface z=x2+3y2?

A: Given: rt=t,t,14t, z=x2+3y2 for finding intersection point of curve and surface we put point t,t,14t…

Q: Let z = g(x, y) f2(3, 6) = 5. f(3 cos(ry), y + e=y) provided that f(3,6) = 3, f1(3,6) = 2, i) Find…

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Q: (a) Prove that M: (x² + y^y° + 3z² = 1 is a surface. (b) For which values of e is M: z(z – 2) + xy =…

A: Consider the provided question, (a)

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

A: From the partial derivative with respect to x and with respect to y

Q: An equation of the tangent plane to the surface z = 4xy² + 3x²y² at the point (1, 1, 7) is: Select…

A: z= 4xy2+3x2y2F(x,y,z) =…

Q: An equation of the tangent plane to the surface 1+y Z = at the point p(1, 7, 4) is 1+x (A) 2(x+1) -…

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Q: Find the tangent plane for the level surface f(x,y,z) = 5x4 + cos (4y) + In (6z) = c at the point…

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Q: Q9. Find the equation of the tangent plane to f(x, y) = x ln(y) +x²y+3 at the point (x, y) = (2, 1).…

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Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent is constant and the…

A: The given curve is y=bexa.

Q: Q9. Find the equation of the tangent plane to f(x, y) = x In(y) + x²y+3 at the point (x, y) = (2,…

A: Consider the equation of the form          F(x,y,z) =0 then the equation of the tangent plane to the…

Q: In Exercises 1–5, find equations for the (a) tangent plane and (b) normal line at the point P0 on…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: w that the equation of the tangent space of f(x, y,z)=Vx² +y° +z* at point (2,3,4) is 1 K, y, z) =…

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Q: Find the equation of the tangent plane to *+ y? at the point (2, –3, 10) the surface z = 4 O x + 4y…

A: We have to find

Q: Find the normal line for the level surface f(x,y,z) = 3x5 + cos (5y) + %3D In (5z) = c at the point…

A: Question is solved.

Q: b) Find equations for the tangent plane and normal line at the point po on the given surface.…

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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 all points on the surface z = 2 + xy at which the normal line is parallel to the line x = 3 +…

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Q: Find the extremum and saddle points of the function f(x, y) = x3 – 3xy + y3 if any. Compute cch of…

A: As per our guidelines,only one question can be solved, Solution for B is given below:

Q: Find equations for (a) the tangent plane and (b) normal line at the point P on the given surface 1)…

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Q: Consider the following. f(x, y) = x2y, (2, 1, 4) (a) Find an equation of the tangent plane to the…

A: Given, equation of the surface z=fx,y=x2y and a point (2,1,4). The equation of the surface can be…

Q: H.W: find the tangent plane to the surface z = Vy -x at the point (1,2,1)

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Q: Find all points on the surface at which the tangent plane is horizontal. (a) z = x³y² (b) z = x² −xy…

A: (a). Given the surface z=x3y2,the tangent lane at a given point is given by :…

Q: Suppose that the plane tangent to the surface z = f(x, y) at (2, 7, 8) has equation z + 8x – 2y =…

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Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

Q: Consider the function f(x, y) = 2xy + x2 + 5 Find the equation of the tangent plane to the surface…

A: given: f(x,y)=2xy+x2+5 find the equation of tangent plane to the surface z=f(x,y) at (-1,1,4)

Q: Given the function f(x, y, z) := 6x²; ´yz + 9x³z z+ 5y²z+2xyz + 4z3 + 10x°y+ 3y² +2z+6 compute Vƒ…

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Q: Find an equation of the plane tangent to the surface xy z2 = 2 at the point (2, 1, -1). О А.х+ бу +…

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Q: (a) Find a function f(x, y, z) which satisfies Vf = (y + 2z, æ + 3z, 2x + 3y) (b) If C' is the curve…

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Q: Show that the surfaces x2 + 2y2 + 3z2 = 3,   x2 + y2 + z2 + 6x − 10y + 14 = 0, are tangent to each…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Suppose we have a surface f (x,y)=x²y+cos (4x) · Which of the following is the gradient of f(x,y) at…

A: First I have found the partial derivatives of f(x,y)  with respect to 'x' and 'y' at point P(π/2,…

Q: Which of the following is the equation of the tangent plane of the z = 3x^2+x-y^2+y surface at the…

A: Equation of tangent plane problem.....

Q: 3. If Ø = 2xyz?,F = xyî – zĵ + x²k and C is the %3D curve x = t2, y = 2t, z = t³from t = 0 to t = %D…

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Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, Yo: 20) is given by the…

A: This is the question from vectors.

Q: 30. The equation of the tangent plane to the surface z = x? – 2y² at x = 1, y = 0 is (а) 2 — : 2т —…

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Q: Consider the following. Z = =DVx²+ y?, 5x - 2y + 3z = 22, (3, 4, 5) (a) Find symmetric equations of…

A: a) Here, f(x,y,z)≡x2+y2-z2=0g(x,y,z)≡5x-2y+3z=22P≡(3,4,5)

Q: Show that the tangent plane to the surface x 2 a 2 + y 2 b 2 = cz at the point P(x0, y0, z0) is…

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Q: The equation of the tangent plane to the surface a2- 3y2 – 22 +3 = 0 at the point (2, -1, -2) is…

A: We will find the equation of tangent plane m

Q: 3) Consider the curve C which is the intersection of the surfaces shown in the attached figure. If…

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Q: For the surface f(x, y, z) = 2*yz, find: The derivative at the point (1,2,1) in the direction of v =…

A: To find the derivative  of the given function f(x,y,z) at point (1, 2,1) in the direction of vector…

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: Which of the following give the symmetric equations of the normal line to the surface xy + yz + zx =…

A: Normal to the surface is a line perpendicular to that surface.

Q: Find the normal line for the level surface f(x,y,z) = 7x5 + cos (5y) + In (9z) = c at the point…

A: The given level surface is: f(x,y,z)=7x5+cos(5y)+ln(9z)Given point is:  (9, 3, 10)

Q: Find the equation of the tangent plane to the given surface at the specified point. z+7=xecosz,…

A: Given: z+7=xeycosz,  (7,0,0)

Q: 40. (a) Let f(x, y, z) = x2 + y2 − xyz. Find grad f. (b) Find the equation for the tangent plane to…

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