Review problems-the rst day, M408D
Name:
Please show all work clearly.
1. How many real solutions are the equation
2x + cos x = 0.
2. If f (x) =
x
0 (1
2
t2 )et dt, on what interval is f increasing?
3. Find the limits of: a. limt
2
1sin t
1+cos 2t ;
b.

Review problems-Test 1, M408D
Name:
Please show all work clearly.
1. Find the following integrals.
2
2
2
cos t dt,
0
sin5 t dt,
t sin2 t dt,
x2
0
dx
,
x2 + 4
xdx
x4 dx
3t 2
,
,
dt,
e x dx,
x1
t+1
x2 7
2. Determine whether each integral is convergence or d

Test 2-review, M408D
Name:
Please show all work clearly.
1. Find the area enclosed by one loop of the four-leaved rose r = cos 2.
1.b. Find the length of r = 1 + sin .
2.Find the radious of convergence and interval of convergence of the series
n=0
n(x + 1