Make the curve y=ax*+bx³+ cx²+ dx+e pass through the points (0,3) and (-2,7) and at (1,4) have a point of inflection with a horizontal tangent line.

Q: Find parametric equations for the normal line to the surfacez=-7x2 -9y2   at the point  (2,1,-37)

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Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y)…

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Q: Find all equations of the tangent line to the common curve of the two surfaces with equations z = x²…

A: follow next step

Q: On the curve y3Dx2 ,find a point at which the tangent is parallel to the chord joining (0,0) and…

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Q: Find the orthogonal trajectories of the family of curves y = ax² + 4ax + 4a, where a being…

A: Orthogonal trajectory: If a curve cuts every member of a given family of curves at right angle, then…

Q: bounded by the curve f(x)= Vx-1, y-axis, line y =1 and line y =

A: We will find the area bounded by the curves.

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

A: Topic- application of derivatives  Tangent to surface

Q: Find the orthogonal trajectories of the family of curves.

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

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Q: Find the equation for the y perpendicular trajectories of the curve family. 1. x

A: perpendicular trajectory

Q: Tangent drawn from the point (4, –3,10) to the intersection curve of z = x² and z = 25 – y² surfaces…

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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: 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: Find the orthogonal trajectories of the family of curves. Sketch several members of each Family y =…

A: The given equation of curve is. We have to find the orthogonal trajectories of family of curve.…

Q: Make the curve y= ax2+bx+c pass through (2,1) and be tangent to the lane y= 2x +4 at (1,6)

A: The given curve passes through (2,1) ⇒1=4a+2b+c                                    (1) And the curve…

Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Find parametric equations for the normal line to the surfacez=ln(3x2 +7y2 +1)  at the point…

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Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 4z2 = 21,    (−3,…

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Q: Find the minimum distance from point (2, 5, -1) and plane 3x + 4y + z = 10.

A: Given query is to find the minimum distance.

Q: Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

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Q: Find the orthogonal trajectories for the family of curves y2 = Cx3 . Use a graphing utility to graph…

A: Given curve is y2=Cx3.

Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: Find the equation of the tangent line to the ellipse 25x2+ y2 = 109 at the point (2, 3

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Q: Find the tangent plane to the surface 8x2+y2+4z2 = 25 at the point ( 1, -1, 2 )

A: To find: The equation of the tangent plane at the point  1,-1,2. The given function for the surface…

Q: Find the equations of tangent plane and normal line to the graph of 9yz – Vx² – 8z = xy² – 26 at the…

A: Find the direction derivative for the function f (x,y,z).…

Q: Find the tangent plane to surface 8x2 + y2 + 4z2 = 25  at the point ( 1, -1, 2 )

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Q: Find the orthogonal trajectories ofthe family of curves: y = ke*

A: As per our company guidelines we are supposed to answer only first question. Kindly repost rest of…

Q: How do I find the bounds in which I integrate a curve that is rotated about an axis?

A: To find the bounds, it is necessary to check whether we have to find the surface area or volume. In…

Q: Calculate the length of the curve defined by x =- Vy(y-3)on the interval 1 < y < 9.

A: x=13yy-3,   1≤y≤9 Differentiating with respect to y, we get…

Q: Find the orthogonal trajectories to the family of curves:

A: Consider the given equation. x2=C-12y2lny2-1 Find the derivative of the function with respect to x.…

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: Find the point (xo, yo) on the graph of y = x + 3x2 + 5x – 3, at which the slope of the tangent line…

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Q: parametrically

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Q: Find an equation of the tangent plane to the surface at the given point. 5x2 + 2y2 + 5z2 = 73,    P…

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Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 7z2 = 27,   (−3,…

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: Find the orthogonal trajectories of the family of circles through the origin with centers on x axis.

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Q: The 50 g bullet travelling at 100 ms-1 strikes the 2 kg block centrally and is embedded within it.…

A: Please check step 2 for the solution.

Q: A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane…

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Q: Locate the points of inflection of the curve 4 ƒ (x) = x²e* -2+ V3 2+ V3 Option 1 Option 2 -2+ v2…

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Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

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Q: Find an equation of the tangent plane to the surface at the given point. x² + y2 – 5z2 = 140, (-8,…

A: We will solve the problem

Q: Make the curve y = ax4 + bx3 + cx2 + dx + e pass through the points (0,3) and (-2,7) and at (1,4)…

A: The curve y=ax4+bx3+cx2+dx+e

Q: 1)Determine the equation of the tangent line to the intersection of the surfaces x²-y=0 and y+z²=16…

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Q: Compute the equation of the tangent plane to the surface: y = 1 - x2 - 2z2 At the point (0, 1, 0)

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent…

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Q: Find the orthogonal trajectories to the family of curves: -1).

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Q: Find an equation of the tangent plane to the surface at the given point. z = 8 - -x (3, -2, 2)

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