Let L be the tangent line to the hyperbola xy = 1 at x = a, where a > 0. Show that the area of the triangle bounded by L and the coordinate axes does not depend on a.

Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: Let L be a tangent line to the hyperbola xy=4at x=7. Find the area of the triangle bounded by L and…

A: Given: L is a tangent line to the hyperbola xy=4 at x=7. To determine: The area of the triangle…

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: Find an equation of the tangent plane and a normal line to the surface z = In Vx2 + y2 at the point…

A: Given that: z=lnx2+y2

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y2, (12,…

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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 equation of the tangent plane at the point (1, 2, 7) to the surface given by x³ sin(z) +…

A: Consider a surface F(x,y,z)=0. Then the equation of the tangent plane to the surface F at the point…

Q: Find the point(s) on the surface at which the tangent plane is horizontal.         z = 2xy + 3x + 5y

A: Given z= 2xy+3x+5yfind partial derivatives w.r.t  'x' and 'y' and put it equal to zero⇒dzdx=…

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (6,…

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Q: Use Green's theorem to evaluate 2y3 dx – x³y2 dy, where C is the positively oriented circle of…

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2+ y², (12,…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5) 2=2y, t at…

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Q: Use Green's Theorem to evaluate the line integral f(e*c - 2y)dx+(5x+ev* dy, where C is the 15. 2cos:…

A: We need to find integral.

Q: find the tangent plane to the surface z = y-x at the point (1,2,1)

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Q: Find the point(s) on the surface z = 5xy, at which the tangent plane is horizontal.

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Q: Find the tangent plane to the surface at the given point. 2x+ 3y z= at P (2, – 1, 1) x+y

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Q: Find an equation for the tangent plane to the surface z = 4xy® + sin(rx) at the point (1, 1, 4)

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Q: Find an equation for the tangent plane to z = cos(x2 + y2) at the point /等,0).

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Q: Show that the tangent at P(x,,y,) on the curve -1 Vx+Jy=Ja is yy, ,=a

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Q: Let L be a tangent line to the hyperbola xy=4 at x=9 Find the area of the triangle bounded by L and…

A: Compute the tangent line as follows.

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y²,…

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Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: Find the point(s) on the surface z = xy + 1/x + 1/y at which the tangent plane is horizontal.

A: Given that: The surface  z = xy+1x +1y  .

Q: Let L be the tangent line to the hyperbola xy = 1 at x = a, where a > 0. Show that the area of…

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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 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx? + y², (6,…

A: here h(x, y)=z then We can represent the function in the phoneF(x,y,z)=0 where F(x,y,z)=z−ln(x2+y2)…

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Find the tangent plane to the equation z = x + 3y – 5y at the point ( – 5, – 5, 125) 2 Z =

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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: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2+ y², (3,…

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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

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Q: Use Green's theorem to evaluate $ 2y3 dx – x3y² dy, where C is the positively oriented circle of…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = L, (1, 2, 2)

A: This is a problem of vector calculus.

Q: Find the equation of the tangent plane to the surface f(x,y)=In(4x²-2xy-y²) at the point P(-1,-1,0).

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Q: Find the point on the surface  z=x2−y2  at which the tangent plane is parallel to the plane…

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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: x² = y + 3y.

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y²,…

A: We have to find the equation of tangent plane

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In V x2 + y², (6,…

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (12,…

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Q: Find an equation of the tangent plane to the surface at the give h(x, y) = In √x² + y², (12, 16, In…

A: we have to find tangent plane

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 area of the surface formed by revolving the cardioid r= a(1+cosθ) about the x-axis

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Q: Find a parametrization of the osculating circle for the parabola y= X sequar when x=1

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

Q: The parametric form of the tangent line to the image of f(t)=⟨4t2,5t,t−2⟩ at t=3 is L(t)=

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Q: The parametric form of the tangent line to the image of f(t) = (3t2,,t – 2) at t = 2 is L(t) =

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

A: The given surface can be written as F(x, y, z)=0, where F(x, y, z)=xy-z