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Internet Security
EE 282 Electrical Engineering Dept. SJSU Dr. Jalel Rejeb
Course Outline/Motivation
2
Let us consider the following example from which we will try to identity some of the main topics that will be covered in this course: Examp
San Jose State University ELECTRICAL ENGINEERING DEPARTMENT EE 281, Computer Networks
Homework 4
Solution
Error: remove the link between LAN A and B2, and B2 should be connected to LAN D, as indicated in "blue"
Math 310 - hw 1 solutions
Wednesday, 2 Sept 2009
1.4 (a) Guess a formula for 1 + 3 + + (2n 1) by evaluating the sum for n = 1, 2, 3 and 4. [For n = 1, the sum is simply 1.] We evaluate the sums for n = 1, 2, 3 and 4 as follows: 1=1 1+3=4 1+3+5=9 1 + 3 + 5
Math 310 - hw 2 solutions
Friday, 11 Sept 2009
4.1 h, j, n, p; 4.8, 4.14 a
4.1 For each set below that is bounded above, list three upper bounds for the set. Otherwise write Not bounded above or NBA. (h) [2n, 2n + 1] n=1 This set is not bounded above (by
Math 310 - hw 3 solutions
Friday, 18 Sept 2009
5.2, 8.2 d, 8.4
5.2 Give the inmum and supremum of each set listed below: (a) S := cfw_x R : x < 0 Since S = (, 0), we have inf S = and sup S = 0. (b) S := cfw_x R : x3 8 Since S = (, 2], we have inf S = and
Math 310 - hw 4 solutions
Wednesday, 30 Sept 2009
8.8a, 8.10, 9.1b;
8.8 (a) Prove the following:
n
lim
n2 + 1 n = 0.
We rst observe that
n2 + 1 + n (n2 + 1) n2 1 n2 + 1 n = = . n2 + 1 + n n2 + 1 + n n2 + 1 + n Let > 0 and set N := 1 . Let n N and suppose
Math 310 - hw 5 solutions
Wednesday, 14 Oct 2009
10.2, 10.6a, 10.10;
10.2 Prove Theorem 10.2 for bounded nonincreasing sequences. Suppose that (sn )n is a bounded nonincreasing sequence and set s := inf cfw_sn : n N (Note that s R). We will prove that sn
Math 310 - hw 6 solutions
Wednesday, 21 Oct 2009
11.6, 11.7, 11.10;
11.6 Show that every subsequence of a subsequence of a given sequence is itself a subsequence of the given sequence Hint: Dene subsequence as in (3) of Denition 11.1. Let (sn )n be a sequ
Math 310 - hw 7 solutions
Wednesday, 28 Oct 2009
17.4, 17.9d, 17.10c; x is continuous on its domain [0, ). Hint: Apply Example 5 in 8.
17.4 Prove that the function x
Let x0 [0, ) and let (xn )n be a sequence in [0, ) such that limn xn = x0 . Then by Exam
Math 310 - hw 8 solutions
Friday, 6. Nov 2009
18.4, 18.6, 18.10;
18.4 Let S R and suppose there is a sequence (xn )n in S that converges to a number x0 S . Show that there exists / an unbounded continuous function on S . 1 for x S. x x0 Then f is continuo
Math 310 - hw 10 solutions
Monday, 30 Nov 2009
29.2, 29.14, 29.18;
29.2 Prove that | cos x cos y | |x y | for all x, y R. Let f : R R be dened by f (x) := cos x for x R. We will use the facts that f is dierentiable on R and that f (x) = sin x for all x R.
Math 310 - hw 9 solutions
Friday, 20 Nov 2009
20.14, 20.20.a, 28.2;
20.14 Prove that
1 1 = + and lim = . x0 x x0 x Let (xn )n be a sequence in (0, ) such that xn 0. We prove that x1 +. Let M > 0, then since xn 0, n there is N such that for all n N, n > N
Math 310 - Quiz 2 Solutions
Monday, 28 Sept 2009
No calculators, notes or text allowed. Each problem is worth ten points. 1. Use the denition of limit to prove that:
n
lim
n1 1 =. 2n + 3 2
Let > 0 be given and set N := Let n N and suppose that n > N . The