(a,b) /a,b Ltt Grou which is defined : (am)なce,d)-(ac, b+d)tor every (a,b), Cc,d) in G. a. tind the idenity etement oG p 4: , a #ols in to the operetion b. tind the inverc (4,1) and (-1, -1) e. t...
Every ring in this test is commutative with 1 and 1 0 1. Which of the followings are prime ideals of Z? (Separate your answers by commas.) A. ( B. (2). C. (9). D. (111). E. (101) 2. Which of the followings are ring homomorphisms? (Separate your answers by commas.) A.φ: Z → Z, defined by (n) =-n for all n E Z B. ф: Z[x] Z, defined by ф(p(z)) p(0) for all p(z) E Z[2] C. : C C....
Which of the following series diverges? n +2 2n -1 n1 n+3 O A. 2 B. O C. 1,3 O D. 1, 2 OE. 2, 3 F. None O G. O H. 1,2,3 Find the sum of the series A. B. OC. 1/10 D. 1/2 3/2 3/4 OE. 1 F. 5/12 OG. 1/4 H. Divergent Which of the following series converges? oo 2n 1.Σ n 1 23n nE1 (n+ 1)3 n+ 1 3. O A. None O B. 2 O...
1. Show that the Lagrangians L(t,q, y) and Īct, 4, ) = L(1,4,0) + f/10, 9) yield the same Euler-Lagrange equations. Here q e R and f(t,q) is an arbitrary function. 2 Lagrangian mechanics In mechanics, the space where the motion of a system lies is called the configuration space, which is usually an n-dimensional manifold Q. Motion of a system is defined as a curve q : R + Qon Q. Conventionally, we use a rather than 1 to...
Q R S T U A B C D E F G H 4 Problem C (26 points): 5 Statue Company is able to produce two products, a Fancy Statue and a Plain 6 Statue with the same machine in its factory. NOTE that only ONE Statue can be 7 manufactured at a time using this machine. The Company currently makes both 8 statues, but management is concerned that this strategy is not providing 9 maximum benefit. They are thinking...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value...
Notes for lab dc02-Resistors and the Color Code will skip are Part 2 e, g: Part 4; Exercises 2, 4,5,6 and 3. It is important to answer the exercises correctly in each labl you should include the appropriate prefix for the unit in the Numerical Value We will not be Volt using the Volt-Ohm meter (VOM) for this lab, so skip the parts that ask for VOM measurements. The parts we You do need to complete Exercises1 Note that in...