Let f(x)=x2+8x. Evaluate f(x)=--16
1 answer:
You might be interested in
Step-by-step explanation:
Domain of a rational function is everywhere except where we set vertical asymptotes. or removable discontinues
Here, we have
First, notice we have x in both the numerator and denomiator so we have a removable discounties at x.
Since, we don't want x to be 0,
We have a removable discontinuity at x=0
Now, we have
We don't want the denomiator be zero because we can't divide by zero.
so
So our domain is
All Real Numbers except-2 and 0.
The vertical asymptors is x=-2.
To find the horinzontal asymptote, notice how the numerator and denomator have the same degree. So this mean we will have a horinzontal asymptoe of
The leading coeffixent of the numerator/ the leading coefficent of the denomiator.
So that becomes
So we have a horinzontal asymptofe of 2
Use Stokes' theorem for both parts, which equates the surface integral of the curl to the line integral along the surface's boundary.
a. The boundary of the hemisphere is the circle in the plane
, where the curl is
. Green's theorem applies here, so that
which means the value of the line integral is 3 times the area of the circle, or .
b. The closed sphere has no boundary, so by Stokes' theorem the integral is 0.