The domain of f(x, y) is the xy-plane, and values of f are given in the...

 

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The domain of f(x, y) is the xy-plane, and values of f are given in the table below. yx 01234 0 50 50 50 50 50 1 48 48 49 49 50 Find fc grad f dr, where C' is (a) A line from (0, 1) to (1,3). So grad f.dr = (b) A circle of radius 1 centered at (1, 1) traversed counterclockwise. So grad f.dr = 2 50 52 54 55 55 3 53 53 55 55 56 4 57 58 57 58 59 Let F=(5xy, 5y) be a vector field in the plane, and C the path y = 4x2 joining (0,0) to (1,4) in the plane. A. Evaluate F. dr B. Does the integral in part (A) depend on the path joining (0, 0) to (1,4)?| Note: You can earn partial credit on this problem. (y/n) Preview My Answers Submit Answers Consider the vector field F = (x+ y, 4xy). C Compute the line integrals F. dr and F. dr, where c(t) = (t, t) and c2(t) = (t, t) for 0t1. Can you decide from your answers whether or not F is a gradient vector field? Why or why not? Je, F. dr = JF dr == Is F conservative? (yes/no) The domain of f(x, y) is the xy-plane, and values of f are given in the table below. yx 01234 0 50 50 50 50 50 1 48 48 49 49 50 Find fc grad f dr, where C' is (a) A line from (0, 1) to (1,3). So grad f.dr = (b) A circle of radius 1 centered at (1, 1) traversed counterclockwise. So grad f.dr = 2 50 52 54 55 55 3 53 53 55 55 56 4 57 58 57 58 59 Let F=(5xy, 5y) be a vector field in the plane, and C the path y = 4x2 joining (0,0) to (1,4) in the plane. A. Evaluate F. dr B. Does the integral in part (A) depend on the path joining (0, 0) to (1,4)?| Note: You can earn partial credit on this problem. (y/n) Preview My Answers Submit Answers Consider the vector field F = (x+ y, 4xy). C Compute the line integrals F. dr and F. dr, where c(t) = (t, t) and c2(t) = (t, t) for 0t1. Can you decide from your answers whether or not F is a gradient vector field? Why or why not? Je, F. dr = JF dr == Is F conservative? (yes/no)