Question

A) Determine curlF of the vector field F=(4x²=3x²y²+2x−y+z). Is F conservative ? Why or why not? You mist use the result involving euriF and fully calculculate it. Show all your work. (2 points)

b) The vector fied F=(2xyx² +2yz,y²) is a conservative vector field (you do not need to show that). Find a potentia function for F. Show all your work (3 points)
c) Suppose that we have the vector field F of Question 8b Consider the curve C :r(t)=(t₂−3sin(πt/2)+cos(π(3+t)/2),tan(πt)−t/ there 1≤t≤3. Use your potential function of 8b and the Fundamental Theorem of Line Integrals over a vectot field to determine ∫F-dr. You must absolutely use the fuadamental theorem. Show all your work. ( 2 points)

Answer 1

The student's question addresses the calculation of the curl of a vector field, determining if it's conservative, finding a potential function for a given conservative vector field, and using the Fundamental Theorem of Line Integrals for computation.

Step-by-step explanation:

The student's question involves concepts from vector calculus, specifically the curl of a vector field and the identification of conservative vector fields. Answers to parts a) and b) of the question require understanding of vector operations such as curl and the potential function for a vector field. For part c), the use of the Fundamental Theorem of Line Integrals is required to compute the line integral of the vector field along a given curve.