x(t) = t², y(t) = t³ – 3t, on – ∞

Q: 32 – x² – 3y² at the 5. Find the equation of the tangent plane to the surface z = point (2, –1, 5).

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Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: Find thee orthogonal trajection of the one-parameter family of curve ex +e-y =c

A: ex+e-y=c

Q: differenetiate parametrically to find dy/dx in terms of t:  x=1/t+1 , y=2t^2-4

A: please use according to form i did solved two equation because your question is not write clear that…

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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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: 4. Find the equation of the tangent plane to the surface Z = = 5tan(x) – sin(3y) at the point (xoyo)…

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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: (a) A beam is fixed at its left end x = 0 but is simply sup- ported at the other end x = L. Show…

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Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

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Q: A particle was following the trajectory r(t) = (e', sin (2t), t), but it starts flying tangentially…

A: SolutionGivenA particle was following the trajectory r(t)= (et,sin(2t),t) , but it starts flying…

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: At time t, the position of an ant moving in the xy-plane is given by parametric functions…

A: Given parametric functions are: dxdt=3t+2dydt=t2-4

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4,…

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Q: 1. Find an equation of the tangent plane to the surface of z = sin(x - 2y) at the point (7,2,0).

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Q: 3. Find an equation of the tangent plane to the paraboloid defined by z= 5x +4y? at the point…

A: The given equation is; z=5x2+4y2 at the point (-1,1,9).

Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

A:

Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: 2 Find the points on the curve ax+ 2bxy + ay = c,ay = c, 0<a<b<c,whose distance from the origin is…

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Q: 4. Find an equation of the tangent plane to the surface z=- xy+8 at the point (1,1,-10) ху — 2х

A: Equation of tangent plane is: {df(x0,y0)/dx} (x-x0)+{df(x0,y0)/dy} (y-y0)-(z-z0)=0

Q: Find the equation of the tangent line to right branch of the hyperbola x = sec t, y tant, -sts at…

A: Given query is to find the equation of tangent line.

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: Differentiate parametrically to find X 1 t-1 y=t³+2 dy dx in terms of t:

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Q: Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

A: Given problem:- Use Green's theorem to evaluate ∫c (xy + y2 )dx + x²dy  by the curve y = x and y =…

Q: Find an equation of the tangent plane to the surface y ln xz2 = 2, at the given point (e, 2, 1) and…

A: Given: ylnxz2=2 at the given point e,2,1

Q: If the equation of the tangent plane to x2+y²-83z2=0 at (1,1,/2/83) is x+ay+Bz+y=0, then a+ß+y=

A:

Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

A:

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx+ x?dy by the curve y = x and y = x2.

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Q: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

A:

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 points (x, y) on the curve with the parametric equations (x3Dt3- 4t at ly=t +2 which the…

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Q: Find parametric equations for the semicircle x2 + y2 = a2, y &gt; 0, using as parameter the slope t…

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Q: 9. Find an equation for the tangent plane and the normal line to the surface xy + yz + zx = 5 at the…

A: f(x,y,z)=xy+yz+zx-5=0,  at  (1,2,1)now we differentiate above equation with respect to x,y,z…

Q: Find the slope of then tangent line to the parametric curve t t2 + 25, y 6. at t = -1 and t = 1…

A: Shown below

Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

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Q: (2² + y² – 1)³ – x²y3 = 0, 2- Given the curve dy find dx -2 2

A:

Q: 2dy -2y 2. zt at

A: Solved below

Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

A:

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 a generating curve on the xz-plane for the surface of revolution with equation x²+ y²+ z²= e2x

A: Solution: Given equation is x^2+y^2+z^2=e^(2x)

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx + x²dy by the curve y y = x2.

A:

Q: Find an equation of the tangent plane to the surface x2 + y2 + z2 = 9 at the given point (1, 2, 2)…

A: Given equation: x2+y2+z2=9 Consider the given equation, fx,y,z=x2+y2+z2-9=0

Q: dy Differentiate parametrically to find dx in terms of t: %3t2, y3 6t

A:

Q: Find an equation of the tangent plane to the surface at the given point. xy2 + 3x – z2 = 56, (5, -3,…

A: Given:   xy2 + 3x - z2 = 56  Point ( 5 , -3, 2 )