PRACTICE EXAMS
- Practice exam for Chapter 6
and Sequences and Series: solution key here (pdf
copy)
- Practice problems for the final: Here are some suggested problems to do
from the textbook (I haven't checked to see if I've assigned any of these
already). I am not planning on writing solution keys to all of these; if you
can do all of these, you are in great shape.
- Chapter 1: 1.1) #13, #15, #22, #25; 1.2) #2, #3, #11, #17, #18; 1.3) #1,
#2, #4, #5; 1.4) #1, #4, #9; 1.5) #1; #14.
- Chapter 2: 2.1) #1, #2, #5, #21, #26, #30; 2.2) #1, #4, #5, #7, #8, #9;
2.3) #1, #2, #4, #8, #15, #18; 2.4) #1, #4, #6, #9, #14; 2.5) #2, #3,
#4, #5, #8, #15, #28 (good problem); 2.6) #1, #2, #4, #6, #10, #19.
- Chapter 3: 3.1) #4, #6, #7, #10, #20, #22, #23; 3.2) #1, #3, #4, #6; 3.3)
#1, #5, #8; 3.4) #1, #5, #10, #18, #20 (good problem), #29 (do distance
squared)
- Chapter 5: 5.1) #1, #7; 5.2) #1, #2, #5; 5.3) #1, #2, #7 (good problem),
#12; 5.4) #1, #2, #8; 5.5) #1, #2, #5, #10, #21.
- Chapter 6: 6.2) #1, #7, #9, #13, #14, #23#26, #29 (good problem).
- Sequences and series problems:
- Find the limit of the following sequences (or prove the limit does not
exist): a_n = (n^3 - 1)/(n^2+n+1); b_n = cos(n) / log(n); c_n = 4n^3-sqrt(n);
d_n = (2^sin(n) + 5)/n^2, cos(sin(n)) / log(n-1). e_n = (6/7)^n; f_n = (4n)! /
(n!^2).
- For the problems in the above exercise, determine which converge. Also
determine if 1/sqrt(n)) leads to a convergent sum, if b_n = (2^n + 3^n) / (4^n
- 5^n) leads to a convergent or divergent sum.
PRACTICE PROBLEMS / SOLUTIONS FOR CALC I/II
REVIEW SHEET FOR THE COURSE