Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (3x2 − 2y2)i + (4xy + 4)j

In this problem, since the condition of equal derivatives does not apply, the vector field is not conservative.

A vector field can be described as:

It is conservative if:

In this problem, the field is:

Then:

Since , the field is not conservative.

A similar problem is given at link

In order for F to be conservative, there must be a scalar function f such that the gradient of f is equal to F. This means

Integrate both sides of the first equation with respect to x :

Differentiate both sides with respect to y :

But we assume g is a function of y, which means its derivative can't possibly contain x, so there is no scalar function f whose gradient is F. Therefore F is not conservative.

answer: 2/4

step-by-step explanation:

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source