Aparticle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field
f(x, y, z) = z2i + 2xyj + 5y2k.
find the work done.

answer: 48

explanation

i assume you mean

there is a piecewise smooth curve that describes the path of this particle. let be the curve that is the path of the particle. to find the work done, we can calculate

let be the line segment from the origin at to . a vector function for is given by for .

let be the line segment from to . let us describe this line segment by a vector function. a direction vector for this line is . the initial vector is . thus a vector function for is for . (we can check the values of and and see that they match with where the initial and final points of the line segment are.)

let be the line segment from to . a direction vector for this line is . the initial vector is . thus a vector function for is for .

let be the line segment from to the origin at . a direction vector for this line is . the initial vector is . thus a vector function for is for .

then we have

now for means that , so

now for means that so

now for means that so

now for means that so

therefore,

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.