problems Review for EXAM II MTH 169
The following is a list of problems that may help you study for the test. This does not mean that the test problems will come from this collection. Note that any material discussed in class is fair game for the test! 1. Evaluate the following indenite integrals: (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) (r) (s) (t) xex dx ex sin x dx cos2 x dx sin3 x cos4 x dx x2 ln x dx x ln x2 dx ln x dx x2 sec2 x tan x dx sec x tan x dx sec2 x tan2 dx sec3 x tan x dx tan2 x dx dx x2 4 x2 ln (2x) dx x cos x dx x2 dx +3 x
3/2
(x2 + 3) x dx x2 + 3 dx x2 x2 3 dx + x2 4x + 4
dx
2. Evaluate the following integrals (if possible)
1
(a)
0
xex dx
/4
(b)
0 1
sec2 x tan x dx
(c)
1 2
dx x3 dx x1 ex dx
(d)
0
(e)
0
(f)
0 0
xex dx xex dx 1 dx 5 x 0 1 dx 5 x 1
1 2 1
(g) (h) (i) (j) (k)
0
1 dx 5 x cos (3x) dx
3. Find the following limits (if they exist): (a) lim (b) lim (c) (d) (e) (f) 1+ 1 x
x
x
ln x x x x3 lim x3 x2 5x + 6 x1 lim x2 2x x2 x1 lim x2 x2 2x ex lim x x2
x
(g) lim (h) lim
x0
x2 ex sin (3x) sin (4x)
4. Find the partial fraction decomposition: 2 9 x1 (b) f (x) = 3 x + x2 x1 (c) f (x) = 2 x x6 2x 3 (d) f (x) = 2 (x 1) (a) f (x) = x2