Let F(x, y) that starts at (0, 0)and ends at (1, 2). (6æ? + 4y) 7 + (4x + 3) j. Calculate la F . dř, where C is the portion of the parabola y = 4x – 2x2

Q: r(t) = ti + (2tt2) intersect the paraboloid (2) At what points does the curve r(t) z = x² + y²?

A: We are asked to find the intersection point.

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 an equation of the plane tangent to the following surface at the given point. z=6-3x- 3y; (2,3,…

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Q: Q4/ Find the abs.max cand abs, min Valuse of the Runctia Kcx, y) = I+xy-3x on the closed regen…

A: We have f(x, y) = 1+xy-3x ∂f∂x = y-3, ∂f∂x = 0, y-3 = 0, y = 3 ∂f∂y = x, ∂f∂y = 0, x=0 So one…

Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

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Q: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: 13. The parabola y = x2 + x + 1 opens: A. To the right %3D B. To the left C. Upward D. Downwarč

A: y=x2+x+1 here parabola is in the form of y=ax2+bx+c which means it can be open up or down…

Q: Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the…

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Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

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Q: Find an equation of the plane tangent to the following surface at the given point. z= 6- 3x - 2y;…

A: The equation of tangent plane to the surface z=fx,y at the point a,b,fb can be calculated using the…

Q: Find the minimum of f(x,y) = 5x + 4y on the ellipsoid 6x2 + 4y2 = 3. Leave your answer correct to t…

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Q: Suppose that the intersection of the graph of z=f(x,y)  with the plane x =1 is a parabola that open…

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Q: .. Evaluate (x+y) dx+xy dy where C is the parabola y = x², x : 0 → 2.

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

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Q: Find the greatest and smallest values that the function f(x,y) = 4xy takes on the ellipse x +2y² = 1…

A: Let's find.

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

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Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = <t, t2>That implies,

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: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

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Q: Find the equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

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Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

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

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Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

A:

Q: Find an equation of the tangent plane to the surface 3x? + 2xy – 4z2 + 2x – 3y = 0 at the point P(0,…

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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 minimum of f(x,y) = 5x + 2y on the ellipsoid 9x2 + 2y2 = 7. Leave your answer correct to…

A:

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

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Q: Find the minimum of f(x,y) = 4x + 3y on the ellipsoid 4x2 + 2y2 = 6. %3D Leave your answer correct…

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

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Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

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Q: Find the point on the parabola x = t, y = t2, -∞ < t < ∞ closest to the point (2, 1/2).

A: Given Data The first equation is x=t. The second equation is y=t². The point is (2,1/2).…

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

A: We have to find the equation of the tangent plane.

Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

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Q: Find the length of the parabola given by c(t) = (t, t2) for 0 ≤ t ≤ 1.

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

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Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: 4x2 dx - xy dy 16x2, y = o from (-1, 0, 16) to (1, 0, 16) (d) dz, where c is the parabola z

A: To evaluate the line integral along the arc C of the given parabola

Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

Q: Find the equation w=T(x,y,z) of the tangent hyperplane at p. F(x,y,z)=3x²-2y²+xz², p=(1,2,-1)

A: General equation for the tangent to the plane is expressed as:…

Q: The tangent and the normal to the parabola y²=20x at the point T(5,10) meet the x-axis at the points…

A: Details solution is given below:

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

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Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

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Q: Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the poin (1, 2, –1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

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

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Q: Let f(x, y) =V2x²+4y2 +32 -x. The domain of c for which the level curve f(x, y)=c is an ellipse is

A: For the solution follow the next step.

Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2