O Evaluate S. F · dr where F = (x², (xy + 4)) and c is the parabola y = x² + 1 om (0, 1) to (2, 5).

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

A: The equation of a curve and a paraboloid are given by, rt→ = ti→+2t-t2k→ and z = x2+y2...1. The…

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: 1 The domain of the function f(x,y)= + In(4- 4x2 - y?) is the region inside the x²+4y² – 4 ellipse…

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Q: Transform the equation rydx – (z+2) dy = 0 into the form of a %3D variable separable f(z) dz + g(y)…

A: Here, the given differntial equation is: xy dx-(x+2)dy=0...(1) To write the eqaution in form of f(x)…

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: At what points does the curve r(t) = t i + (6t - t2)k intersect the paraboloid z = x2 + y2? (Enter…

A: Given: Equation of curve:                                    r(t)=t i +(6t-t2) k Equation of…

Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

A: Tangent line equation problem....

Q: Study the analytically of w = L(2) at the points z = 0, z= v2,z = -21

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Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

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Q: c) x+2y) dA, where D is bounded by the parabolas y=2x2 and y =1+x?.

A: C) The area D bounded by the parabolas y=2x2 & y=1+x2 is as shown below. The red graph is of…

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: At what points does the curve  r(t) = ti + (5t − t2)k  intersect the paraboloid  z = x2 + y2

A: We have to find the intersection point

Q: The orthogonal trajectories to the family of hyperbolas xy= C is given by the family 1)y=cx 2)y2 -x2…

A: We need to find the orthogonal trajectory to the family of hyperbola xy=c

Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z =x^2 +3y^2,…

A: z=x2+3y2 , x=1 at the point (1,2,13)

Q: 4. Find f such that F = Vf and use it to evaluate SF. dr. (a) F(x, y) = (3 + 2xy²) î+ 2x²y ĵ, C is…

A: (4) To find: f such that F→=∇f and To Evaluate: ∫CF→·dr→. For the following Functions: (a)…

Q: Q) Fit a second-degree parabola for the following :data 4 3 2 1 0 x 6 5 4 3 1 Y Using Y=a+bX+cX2 Y=…

A: The regression analysis is done to fit a dataset into an equation. A graphing utility can be used to…

Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

A:

Q: 3. Let R be the region below bounded by the parabola y = 4x² and the lines 3x - 2y +3=0 and y = = 0.…

A: Follow the procedure given below.

Q: Calculate 127 y [1/10 ds where C is the parabola r(t) = (t, t², 0). Let 1 ≤ t ≤ 4. X

A:

Q: If F = (2z+ y,z, 2y+x) and S is a unit square in the yz-plane with its normal in the positive…

A: Consider the given vector F.

Q: Find a parametrization c(t) of the line y = 5 − 2x such thatc(0) = (2, 1).

A: This question comes under the category of calculus and from the parametrization of the line here we…

Q: Find the best quadratic approximation, Q(x, y) of V9 – 6x – 4y for (r, y) near (0,0).

A: We have to find the best quadratic approximation Q(x,y) for (x,y) near (0,0).

Q: 8. Calculate fo F • dr, where F(x, y) = y² i + (6x + 6y)j, and C is the portion of the parabola 2y²…

A: Given curve is 2y2-x=1 and points are (1,-1) to (7,2)

Q: Vf(x, y) = 4y sin(xy)i + 4x sin(xy)j, F = V f(x,y), and C' is the segment of the parabola y = 5x²…

A: According to the fundamental theorem of line integral, for a smooth curve C given by r→t, a≤t≤b,…

Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: 1. Compute SF · dr where F(x, y) = (y²,–x²) and C is the part of th parabola u = 12 from (-1 1) to…

A: First take dot product of f and dr Then put value of y in terms of x Integrate and raise limit of…

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: 4. Consider the equation of the hyperbola given by x2 + 2xy – y² = 7. Find an equation of the…

A:

Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

Q: Q4/Find the abs.max and abs.min valuse of the huctu f,y) = \+xy-3x on the cosol regen oounded by the…

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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: 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: Given f(x, y) = x² - 4y, the parabola x² - 4y - 2 = 0 is the level curve of fat 02 0-2 01 00 None of…

A: Ggg

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: Let F(x, y) = (x + 1)j, and let C be the portion of the parabola y = x² that starts at (0,0) and…

A: The integral ∫CF⇀.dr⇀ is positive. From the graph the angle between direction of F⇀ and dr⇀  is…

Q: Which of the following points do not lie on any tangent line of the parabola y = x2 + 2? (2,6) O…

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Q: Show that the graph of ř = (t sin t, t cos t, t²) lies on the paraboloid z = x? + y?.

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Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: (b) Given  = (x²y)î + (xz – z²)f – (xyz)k, determine the following at point (1, 1, 2): (i) V- Â.…

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Q: Find the equation of tangent line to the parabola y² = 6x – 3 which is perpendicular to the line x +…

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Q: Obtain the Solution x, y > 0, xy > 1 of the PDE 2y on the x+y 1 Uxy such that u = x+y 0, ux…

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Q: Q2) Find the equation of the tangent to the hyperbola x? – 3y² = 1 at the point S(2,-1). %3D A) 2x +…

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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: Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(ry)j, F = Vf(x,y), and C is the segment of the parabola y =…

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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

Q: Find eauation of ny Perbola at o Ne tne foci Fz the and crankshafto f Fi Fz ny Perbola= Fi F

A:

Q: 16. Evaluate (x + V9) ds where C consists of two segments: the part of the parabola y = x² from…

A: In the given question we have to evaluate the integral ∫C(x+y)ds where C is the regionconsist of two…