Answer:
Step-by-step explanation:
The average value theorem sets:
if f (x) is continuous in [a, b] and derivable in (a, b) there is a c Є (a, b) such that
, where
f(a)=f(π/2)=-4*sin(π/2) = -4*1= -4
f(b)=(3π/2)=-4*sin(3π/2) = -4*-1 = 4


⇒

c≅130
For this case we must find the domain of the following function:

By definition, the domain of a function is given by all the values for which the function is defined.
In this case, the argument of the expression must be greater than 0 to be defined.

Thus, the domain of the function is given by all the values of x greater than -2.
Answer:
Domain: 
Answer: Using the proportions between the segments, the area of the triangles are:
1. Area of triangle ADC is 25 in^2.
2. Area of triangle BDC is 15 in^2.
3. Area of triangle CDE is 12 in^2.
Please, see the attached files.
Thanks.