5. (20 pts) Evaluate the following sums. The delta below is a Kronecker delta. n=-oo n2sin...
(5 pts) For the graph below, use right side Riemann sums to find the area under the curve to the x-axis from 0 <x6 and n = 3 Area =
cos((+dt. (5 pts.) 1 3. Evaluate the integral 8(t)dt. (5 pts.) 4. Evaluate the sum Σ 23]n]. (4 pts.) 2 +2 +2 + 2+2 4 2
just simplyfy n expand
1.(20 Pts) Factor to obtain a product of sums. Simplify where possible. F(WXYZ)- W'Y'Z' +WXZ + W'YZ+X'Z 0 0
5. (20 pts). Solve the following initial-value problem: Ut + 2uuz - 0<x<, 0 <t<oo 0 1 <1 > 1 u(t,0) = Then draw the solution for different values of time.
,n2} with ISI = n. 4. Let n be a positive integer with n > 20, and let S {1, 2, -I with a) Show that S possesses two dilferent 3-element subsets, the sums of whose elements are equal. (b) Show that S possesses two disjoint subsets, the sums of whose elements are equal
,n2} with ISI = n. 4. Let n be a positive integer with n > 20, and let S {1, 2, -I with a) Show that...
5. (12 pts.) Evaluate the following triple integral where the region E lies above the cone 32+32 and below the sphere +y2
5. (12 pts.) Evaluate the following triple integral where the region E lies above the cone 32+32 and below the sphere +y2
4. (20 pts) Let {xn} be a Cauchy sequence. Show that a) (5 pts) {xn} is bounded. Hint: See Lecture 4 notes b) (5 pts) {Jxn} is a Cauchy sequence. Hint: Use the following inequality ||x| - |y|| < |x - y|, for all x, y E R. _ subsequence of {xn} and xn c) (5 pts) If {xnk} is a See Lecture 4 notes. as k - oo, then xn OO as n»oo. Hint: > d) (5 pts) If...
(10 pts.) (5 pts. (5 pts.) 3. Soils in the rice paddies of Mekong delta have been continuously submerged and used for growing rice. These soils developed on pyrite (FeS.)-rich former marine deposits. During this process, SO and Fes are being released into the environment. Answer the following questions: (a) Assuming that the oxidation state for Sin Fes, is -1, write the balanced half reactions for Fe and S. (b) Write the complete redox reaction for this system. (c) Using...
Question2 0/5 pts If exact running time of an algorithm is T(n)-5n3+ n2 + 3n -5 where n is the input size, then which of the following is true? T(n)- O(n) RCOECEQuestion 3 0/5 pts Which of the following is the correct ranking of the functions listed below: logn. n2 n2n, 2. 1500. nlogn, 5 Question 4 5/5 pts to search
Question 1
1. [5 pts] Give a complete definition of lim f(x) = -oo if... 2. [25 pts] Give an example of each of the following, or state one or more theorems which show that such an example is impossible: a. A countable collection of nonempty closed proper subsets of R whose union is open. b. A nonempty bounded subset of R with no cluster points. c. A convergent sequence with two convergent subsequences with distinct limits. d. A function...