Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.
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Q: Find the points on the surface xy + yz + zx - x - z2 = 0 where the tangent plane is parallel to the…
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Q: Calculate the directed derivative of the function f (x, y) = (y^2)/x on the ellipse 2x^2 + y^2 = 1…
A: The given function is fx,y=y2x and the ellipse 2x2+y2=1 Directed derivative,…
Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…
A: We are given the polar curve: r = 1- cosθ use formula: x=r cosθy=r sinθ then, dxdθ=-sinθ+2…
Q: A point moves along the intersection of the elliptic paraboloid z = x² + 3y² and the plane y = 1. At…
A: Point moves along the intersection of the elliptic paraboloid z=x2+3y2 and the plane y = 1. We have…
Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.
A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…
Q: In(xy) cos(Tx + T) when x 2 and y = 1/2.- Find the tangent plane to f(x, y)
A: We have to find the equation of tangent plane.
Q: Find the slope of the tangent line to the curve of intersection of the graph of z = 2x2 + 3xy + 2y2…
A: We need to find slope of the tangent line.
Q: Find an equation for the tangent plane to the surface z + 1 = xy² cos(z) at the point (1, 1, 0)
A: The given equation is z+1=xy2cosz. The objective is to find an equation for the tangent plane to the…
Q: Find an equation for the tangent line to the curve given parametrically by x(t) 2t, y(t) 4t2 +t+ 3 =…
A: we want to find the tangent lines to theparametric equations given byx=f(t) y=g(t)The equation of…
Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)
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Q: Find an equation of the tangent plane to the surface z=8/2x+4y at the point (2,1,1). z=
A: Please see the explanation below
Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.
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Q: Find an equation of the normal line to the surface given implicitly by z = sin(xy) at the point…
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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — Зху — у?…
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Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -
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Q: Find one normal vector of the tangent plane to f(x, y) = cos(x² +y²) at point P(1,1, cos 2).
A: As we know the expression of the normal vector to the tangent plane at a point on the curve can be…
Q: Find an equation of the plane tangent to the surface sin(xyz) = at the point (T, 1,-)
A: sinxyz=12 at the point π, 1, 16. Consider, sinxyz=12⇒xyz=sin-112⇒xyz=π6⇒z=π6xy Differentiating…
Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).
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Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.
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Q: Find the directional derivative of the scalar function of (x, y, z) = xyz in the direction of the…
A: Given surface is z=xy
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: Suppose that the plane tangent to z = f(x,y) at (-2,3,4) has equation 4x + 2y + z = 2. Estimate…
A: As the given plane tangent to z=f(x,y) at (-2,3,4) is 4x+2y+z=2, that is z=2-4x-2y thus the…
Q: The parametric equations of a curve are given by x = In (VE +1) and Vt + y = cosh-(2t). X = dy when…
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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 derivative of f (x, y,z) = xyz in the direction of the velocity vector of the helix…
A: Answer and explanation is given below...
Q: Compute the directional derivative of f(r. y) = = at the point (1, 1) in a irection normmal to the…
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Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…
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Q: Find the tangent plane to the graph of **yz +z'e* -y² = 5 at (1,3,2).
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Q: Find the tangent plane of the function f(x, y) = √2x² + 2y² at (1,1). Is it parallel to 2- the plane…
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Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…
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Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)
A: Given; z=2ycos(5x-4y) at the point (4,5,10)
Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…
A: Given:
Q: Find the tangent plane for the level surface f(x,y,z) = 7x5 + cos (5y) + In (9z) = c at the point…
A: Answer: In oerder to use gradients we introduce a new variable c= 7x5+cos(5y)+ln(9z) Therefore the…
Q: For rigid-body motion, the strains will vanish. Under these conditions, integrate the strain…
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Q: Find an equation for the tangent plane to the surface z + 5 = xy" cos (2) at the point (5, 1, 0)
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Q: 2dy -2y 2. zt at
A: Solved below
Q: Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x –…
A: Given that: z=x2-2y2 and point is: (1, 1, 1)
Q: Find the equation of the tangent plane to the surface 2x^2 -xz + y^2 -zy = -5 at the point (1, 3, 4)
A: First we find out partial derivative at given point and then find the equation of the tangent plane…
Q: 3. Find an equation of the tangent plane at P = (0, 3, –1) to the surface with equation ze" + elz+1)…
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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: Find an equation for the tangent plane to the surface z +4 = ry" cos(2) at the point (4, 1, 0).
A: Use the partial differentiation for finding the tangent plane.
Q: Find the equation of tangent plane to the surface z = ln (3x²) + 2y at A (1,0, In (3)).
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Q: Find the tangent plane and normal line equations to x+y +z =1 at the point (1, %3D -2, -4).
A: This question is related to 3D geometry and equations of plane and lines, we will solve it using…
Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.
A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…
Q: Find the equation of the tangent plane to the surface y = 2x² – z² at the point (0,-1, 1)
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Q: Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to (1,3).
A: We have to calculate the integral ∫Cxydx+3y4dy Where C is the curve in the xy plane, x=y2 from 0,0…
Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).
A: To find a tangent plane to the given curve at the point (7,-5,5)
Q: Suppose that r is the position vector of a particle moving along a plane curve and dA / dt is the…
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- Compute the equation of the tangent plane to the surface: y = 1 - x2 - 2z2 At the point (0, 1, 0)A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane x=1. At the point (1,–2,5), itu event off on the tangent line. Where do the bee hit the xz-plane?Find the tangent plane to surface 8x2 + y2 + 4z2 = 25 at the point ( 1, -1, 2 ).
- Find an equation of the tangent plane and symmetric equations of the normal line to thesurface zx2 − xy2 − yz2 = 18 at the point (0, −2, 3)) Compute the directional derivative of f(x, y) = x2y at the point (1, 1) in adirection normal to the ellipse x2 + 2y2 = 1 at the point (1, 0).Find the orthogonal trajectories for the family of curves (enter your solution in the form: F(x,y)=c or y=F(x,C) Where C is a needed constant