Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

Q: Find the abscissa on the curve x²=2y which is nearest to a point (4, 1). А. 0 С.2 В. 1 D. 3

A: Use the distance formula then minimise using derivative.

Q: Find a direction in the xy-plane in which f(x, y) = e¹-xy has zero change at the point P(1.0. e).

A: We know directional derivative formula Du→fa, b, c=∇fa, b, c.u^ Lets say u→=cosθ, sinθ be the…

Q: Find an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

A:

Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

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

A:

Q: Find the equation of the tangent plane to the surface - 8x3 + 7y³ + 3xy at the point (2,0, 64).

A:

Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Find . F dR such that F(x, y) = (2y, xy – 2x) And I is the curve in the 3rd quadrant from the point…

A:

Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

A:

Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -

A:

Q: (d) The curve y = x – x² from r = 0 to r = 2

A:

Q: Find an equation of the plane tangent to the following surface at the given point. z = 6 - 4x2 - y2;…

A: By using equation of tangent plane for surface, we calculate the required tangent plane.

Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

A:

Q: Find the points on the surface z2 = xy + 4 closest to the origin.

A:

Q: Find the equation of the plane tangent to the surface of Z= x2+ Y2 at point P(125)

A:

Q: Find an equation of the tangent plane to the surface 4x^2 + 9y^2 − z^2 = 14 at P = (2, 1, 4).

A: Given,4x2+9y2-z2=14at P=(2,1,4)

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: 3. z = (c

A:

Q: Find the equation of the tangent plane to the surface y = 2a2- z2 at the point (0,-1, 1)

A: Here is the solution

Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

A:

Q: ) Find the gavea d the rgion enclased by the line x-In3 and the curves y= ex and y=ex

A:

Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2  at the point   (2,1,-36)

A:

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

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: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x)) and C is the curve in the third quadrant from…

A: Given

Q: Find the equation of the tangent plane to the surface z = 6x4 + 5y + 3xy at the point (-3,0, 486). z…

A:

Q: Find the equation of the tangent plane to the surface 2 = r - 2r'y+ 2r y at the point where x = 1…

A:

Q: Find the equation of the tangent plane to the surface of the equation z = x2 + y2 - 2xy on the point…

A: Equation of tangent plane

Q: Find an equation of the plane tangent to the following surface at the given point. z= 3- 3x -y:…

A:

Q: Find the points on the curve x2 + xy + y2 = 1 in the xy-plane that are nearest to and farthest from…

A:

Q: Find the point at which the line F (t) = +t intersects the yz plane.

A: Given: An equation of a line in the parametric form is, r→t=&lt;2,-7,7&gt;+t&lt;-5,-6,6&gt; The…

Q: Find the equation of the plane that passes through the point (2, 1,2) and is tangent to the surface…

A:

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

A:

Q: Find the equation for the tangent plane to the surface z= In (7x + 10y + 1) at the point (0,0,0).

A:

Q: Find the equation of the plane tangent Z= x2+ Y2 at point P (1,2,5) to the surface

A: Equation of tangent plane on the surface z=f(x,y)  at the point (a,b,c)  is given…

Q: Find the equation of the tangent plane to the surface 9x +36y +4z? = 108 at the point (-2,1,-3).…

A:

Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: (c) Given that y = x4 – 8x²

A:

Q: Find an equation of the plane tangent to the surface z2 - xy = 14 at (2, 1, 4).

A:

Q: Let f(x, y)=sqrt(2x²+4y² +8) -x. The domain of c for which the level curve f(x, y) = c is an ellipse

A:

Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 6x² + y² -…

A: This question is based on finding equation of plane to the given surface at a point.

Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

A:

Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

A:

Q: find the under the curve y=7-t^2 and above the t-axis

A: