What are
and
supposed to be? Can't answer a/b without that information.
I'll come back to part (c) in a moment. If we can show
is conservative, this part will be a breeze.
For part (d), to show whether
is conservative, we have to show that there is a scalar function
such that
. It appears that you've written
I'm not sure what to make of the
that follows.
means that
Integrating the first PDE with respect to
gives
Differentiating with respect to
gives
But we assumed that
is a function of
alone, which means there is no solution for
, and therefore no solution for
. Hence
is not conservative.
Back to part (c).
is not conservative, so we have to compute the line integral the "long" way. Replacing
and
, we have
If you begin with the basic equation of a vertical parabola: y-k=a(x-h)^2, where (h,k) is the vertex, then that equation, when the vertex is (-3,-2), is
y + 2 = a (x + 3)^2. If we solve this for y, we get
y = a(x+3)^2 - 2. Thus, eliminate answers A and D. That leaves B, since B correctly shows (x+3)^2.
Answer:
x= -5
Step-by-step explanation:
f(x) = [ x^2 - 25 ] / [ x + 5 ] = [ (x + 5) ( x- 5)] / [ x + 5 ] = x - 5
This will be the graph of f(x) = x - 5 with a "hole" at x = - 5
1/6008
is the answer I believe