R
Determine the value of the indefinite integral xe4x dx
To solve this problem we are going to use the method of integration by
parts:
Z
Z
u dv = uv
v du
For our problem u = x and dv = e4x . From this we can determine
du = dx and that v = 14 e4x
We deter
Determine the values of the sides a and b of a rectangle with
perimeter p that will maximize the are of the rectangle A. Determine the maximum area.
Recall the area of a rectangle is determined by the formula:
A = ab
We need to solve for one of the sides
Practice Problems for Final
(1) Take the derivative of the following functions using any method.
(a) f (x) = ex
(b) f (x) = cos(2x + 3)
x2
(c) f (x) = e 2 +3x
(d) f (x) = ln(ex + e x )
(e) f (x) = cos(csc(x)
(f) f (x) = xx
(g) f (x) = aax , where a > 0 is
11 TR
1e-09/02/15
Aaron Morris
I expanded my command window and figure 1 to better show the operations that I did to result in my
answers.
11 TR
1e-09/02/15
Aaron Morris
11 TR
1e-09/02/15
Aaron Morris
11 TR
1e-09/02/15
Aaron Morris
I expanded my command window and figure 1 to better show the operations that I did to result in my
answers.
11 TR
1e-09/02/15
Aaron Morris
11 TR
1e-09/02/15
Aaron Morris