4) Let F(x, y) = yi+xj. a) Show that F is conservative and find a function f such that F = = Vf. b) Use part a) to evaluate fF.dr along C, where C'is the arc of the curve y = x4 – x³ from (1,0) to (2,8).

Q: 21 Let F(x, y) = (3x + 2y)i + (2x - y)j. Evaluate F. dr where C is the curve X y from (0, 0) to (1,…

A: Here we calculate the integral along the curve x = y2 from (0,0) to (1,1)

Q: ii) Let C be the unit circle and N be the point (0, 1). The stereographic projection maps any point…

A:

Q: Which of the following is dy for the curve dx defined by x° – y³ = 2xy? 3x2-2y а. 2x+3y2 3x2-2y b.…

A: Find the derivative of the given curve and match with the correct option.

Q: a. Find a function (f(x,y,z)) such that (F = Vf(x,y,z))? b. Use part (a) to evaluate (F. dr ) along…

A: We have to evaluate the ∫CF.→dr→.

Q: Let fcxry)= 2X sinly)+3X Cos CY ). Find the tangent Plane at the point 2,0).Use the tangent Plane to…

A: In this question, concept of tangent plane at any point is applied. Tangent Plane Naturally, it…

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A: We have to choose the correct answers of two questions.

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: 5) Let F(x, y, z) = (z − x², xz, y²) and C be the curve of intersection between x² +3y² 1 and z = x²…

A: Let us first parameterize curve C.

Q: Compute f ds for the curve specified. f(x, y) = V1 + 9xy, y = x3 for 0 < x < 2.

A:

Q: How would you evaluate |F-dr, where C is the curve with param etrizati on r(t) for astsb?

A:

Q: F(x, y) = x² i + y² j C is the arc of the parabola y = 4x² from (-1, 4) to (0, 0) %3D (a) Find a…

A:

Q: Which of the following is/are points on the curve y-x Br+ 22x - 24x +9 whore the tangent line is…

A: We need to find the points on the curve where the tangent line is parallel to the x-axis.

Q: Let C1 be the curve r(x)= (x − lnx )i + (x +lnx )j, 1<=x<=e, and let C2 be the curve of y=et,…

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Q: Prove that for the curve x = 31, y = 3 f², z = 2 8³, 3 (1+21²) 2 p=-o=

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Q: Draw the curve and find the length in range [0,27]: r(t) = acosti + asentj + btk

A: Given: rt=acosti+asintj+bt

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Q: Let f(x, y) = x² + y? and C be the curve along y = x² from (0, 0) to (1, 1).

A:

Q: Use Green's Theorem to evaluate | F. dr, where F = (Va + 5y, 2x + Vỹ ) and C consists of the arc of…

A:

Q: Let C be the curve in the x-y plane defined by the equation (x – h) + v – k)* =? where h, k, and r…

A: Equation of the curve is x-h2+y-k2=r2 &amp; a, b is a point on the given curve. a). Slope of the…