Use the slopes of the slanted Lines of AABC to find exact f inscribed squore DEFG coordinatesof A=(o,0) B= (2,4 C= (5,0) %3D %3D

Q: Find the equation for the tangent plane at the point Po = (1,2, 2) on the surface x + 4y2 + 22 = 25.…

A: Equation of the Surface x2+4y2+2z2=25 point 1,2,2

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

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Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

A: Given data: First curve xy=3. Second curve x2=9y.

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0). O…

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y?, (6,…

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Q: mine an equatio

A: Here we have to find the equation of rectifying plane to We have,

Q: Find the coordinates of W. When point W lies on UV such that UV:VW is 5:2

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Q: * Find the equation of the tangent plane to the surface 9a2²-12xy = 5x2+5 at the ivon Ni Smob point…

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Q: Find the plane tangent to f(x,y)=x/(x+y) at the point (1,5).

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Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing tat t-0. =…

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Q: Find the distance from point P(1,1,1) to the pl r +y +z = 1

A: We have to solve

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

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Q: 4. y = x2--Inx x = 1 ve x = e

A: Topic- application of derivatives to find angle between curves

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

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Q: Find the slope and concavity of the curve at the given points. r = 1/u, u = -pi, 1

A: Solution:Given    r=1u, u=-π,1To find the slope and concavity of the curve.Formula:Slope of the…

Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

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Q: Where should the point P be chosen on line segment AB so as to maximize the angle θ? (Assume a = 3…

A: Given : a=3, b=4  and c=7 Let BP=x . So , PA= 4-x

Q: Find the tangent plane at P = (xo, Yo, Zo) = (1,2, 8) to the graph of f(x,y) = 2x?y+ y² %3D

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Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 3…

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Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

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Q: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

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Q: Find the tangent plane to the equation z 5z° + 4y – y at the point (4, 2, – 66)

A: Given: z=-5x2+4y2-y      4,2,-66

Q: Find the exact length of the curve. y = In(sec(x)), 0 <x< a/6

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Q: Find the points on the graph of f(x, y) = 3x 2 - xy - y 2 at which thetangent plane is horizontal.

A: Given that, fx, y=3x2-xy-y2z=3x2-xy-y2

Q: A coast artillery gun can fire at any angle of elevation between 0° and 90° in a fixed vertical…

A: A coast artillery gun can fire at any angle of elevation between 0° and 90.

Q: Determine the natural cubic spline that interpolates the data f(0) = 0, f(1) = 1, f(3) = 4 %3D and…

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Q: C is the part of the circle of radius 3 in the first quadrant from (3,0) to (0,3) and F = (1, -y),…

A: Given, C is part of circle of radius 3 in the first quadrant from (3,0) to (0,3) and F=[1,-y] The…

Q: Find the acute angle 0 between the curves C1 and C2 given by C1 : y = x2 , C2 : y = x³ (1) at their…

A: Please refer the attached image for complete solution.

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 3…

A: Given query is to find the position of P to maximize the angle theta.

Q: Find the tangent plane to the equation z - 3x? – – 108) 4y? + y at the point (5, 3, z =

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Q: Integrate counterclockwise around the unit circle (|z| = 1) and choose from the options below that…

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Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: Find the length of the curve. y = In(secx), 0Sx</4

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Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

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Q: Find the tangent plane to the equation z = x2 + 5y² + 3y at the point (-5,-2,39)

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Q: Find the equation of the tangent plane to the surface 4 = 1 16 at the point 9. (1,-3,2)

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Q: Determine the orthogonal trajectories of the family of circles (equation below) that is tangent to…

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Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: integrate ƒ over the given curve. ƒ(x, y) = x2 - y, C: x2 + y2 = 4 in the first quadrant from (0, 2)…

A: The given curve C is a circle with center at origin and radius of 2 units. Let the parametric…