Problem 1. Let A be an infinite set such that |Al S INI. Prove A IN (Hint: First prove this for all infinite subsets B CN. Prove the general case by observing there is a bijection between A and some infinite subset of N.) Problem 1. Let A be an infinite set such that |Al S INI. Prove A IN (Hint: First prove this for all infinite subsets B CN. Prove the general case by observing there is a bijection...
prove 3)1/5, thenf(10)(0)=(145). 101. 16. Let f(x)=x(1+x 3)1/5, thenf(10)(0)=(145). 101. 16. Let f(x)=x(1+x
System dynamics course. Let a transfer function H be 1000s + 10) 100+1000 Use H to respond to the following questions and imperatives a. Write H as a product of standard-form transfer functions Find the frequency response function H(jaw) without simplifying c. Use the axes below to sketch the Bode plot of H. 20 -20 10-1 10° 101 102 103 10 w (rad/s) 90 45 45 -90 -135 -180 10-T 100 101 102 103 101 w (rad/s) Let a transfer...
Question 4 11 pts Each blank is 1 point) 0 Let A - 0 0 3 (al. Find (A) where A, means A, with = 2 (b). For what value of x is A, + I not invertible? or (Please fill it in from small to large for this two blank). Please write the answer to the following problems and upload the answer in one pdf ble after you finish and submit this final (12 points) Lett be a linear...
6. (10 pts) Is L regular? Either prove that it is not regular using pumping lemma, or describe an RE for it. The alphabet of the language is 10,1, +,-) L = { x = y + z | x, y, z are binary integers, and x is the sum of y and z }. For example, strings 1000 = 101 + 11, 0101 = 010 + 11, and 101 = 101 + 0 are in the language, but strings...
Let 0 <10 <yo and In+1 = Vonyn Yn+1 = = (en + yn). Prove that 0 < xn < In+1 < 4n+1 < yn and lim x, = lim yn. n1
Let (IP) be the following integer program: max (0, -1). s.t. 1-1 -107 -10 10 -11</-0.5 1-10 / 0 z integer Let (LP) be the LP relaxation of (IP). We draw the feasible region of (LP) here. 2. . . . . . . to (LP), and prove that it is optimal by providing a (a) Determine an optimal solution certificate of optimality.
2.21 Let Q(2) = VI, which is defined for all x > 0. Prove: Q E C[0,0). (Hint: If a > 0, and € > 0, we seek 6 >0 such that 3 > 0 and - al <& implies Q(x) - Q(a) < €. Begin by showing that|vx-Val' <lt - al.)
31 (a) If fis integrable, prove that fa is integrable. Hint: Given e>0, let h and k be step functions such that h f k and j (k-h) < ε/M, where M is the maximum value of Ik(x) +h(x)]. Then prove that h and k2 are step functions with h' srsk (we may assume that OShSSk since f is integrable if and only if I is-why?), and that I (k2 - h2) <e. Then apply Theorem 3.3. (b) If fand...
HINT 1)-Write a method to accept n integer number between 0 and 100 and return the average. 2)-Write a method to convert an the letter grade as follow. integer number between 0 and 100 to latter grade A to F and return. 100-90->A 89-80->B 79-70->C 69-60->D 00-59->F 3)-Write a method to compute GPA for following letter grade and return the GPA value. A =>4.0 B ->3.0 C->20 D->1.0 Hint for option 1 1 import java.util.Scanner 2 public class ProjPart2 3...