Given a sequence of closed intervals Lai,Dil, such that [a,ba2,b2l 2 [az,b3l, show that there is...
8. Show that Theorem 3.1, the Nested intervals theorem, may be proved as a direct consequence of the Cauchy criterion for convergence (Theorem 3.14). (Hint: Suppose I. = {x: 0, <x<bn} is a nested sequence. Then show that {an} and {b} are Cauchy sequences. Hence they each tend to a limit. Since b.-4, 0, the limits must be the same. Finally, the Sandwiching theorem shows that the limit is in every 1.] Definition. An infinite sequence {n} is called a...
Consider the construction of the Cantor set C c [0, 1] In the st step we remove the open interval (, ) ad are left with two closed intervals [0· and [릎,1]. Let J1 denote one of these two closed intervals. In the 2nd step, we divide J into three intervals and remove the open middle third interval. We are left with two closed intervals inside J. Let J2 denote one of these two intervals. For example, if Ji were...
2. Given that u., and ware three solutions of the linear system Az = b. Verify that the vector cu+du+ (1-c-d)w is also a solution of Ar = b for any scalars DER - 2 1 1 Let A = 1 1 - 2 1 Determine whether the system Az = b is consistent for every beR. 1. Let A and B be two nx matrices. Suppose that AB is invertible. Show that the system Az = 0 has only...
2. Let {xn}nEN be a sequence in R converging to x 0. Show that the sequence R. Assume that x 0 and for each n є N, xn converges to 1. 3. Let A C R". Say that x E Rn is a limit point of A if every open ball around x contains a point y x such that y E A. Let K c Rn be a set such that every infinite subset of K has a limit...
Find a closed form of the recurrence given by an = -6+12-an-1; do = 2. Show work.
1) The root locus trajectory intervals on the real axis. 2) The
number of asymptotes and their center. 3) The breakaway/break-in
point of the locus and its open loop gain. 4) The limit gain for
stability and the value of the closed-loop poles. 5) The gain and
the value of the closed loop poles for a damping ratio of .5.
process with negative feedback: R(s) E(s) C(s) H(s) Go(s)= K, Gp(s)- H(s) 1 s(s+1)2 Determine: 1) The root locus trajectory...
To receive full credit on the confidence intervals, you must show each of the following: a. The critical value (3 points) b. The margin of error (round answers to at least hundredths) (3 points) c. The minimum and maximum numbers of the interval (3 points each) To receive full credit on the interpretations, you must include information about the specific problem. When finding the sample size, remember to round all answers up to the next highest whole number Show all...
2. (8 pts) In contrast to the Heine-Borel Theorem in R", show that the closed unit ball in f = {(21,..., In, ...): -10 < } is not compact. (Hint: find a sequence on the unit sphere containing no convergent subsequence)
1)this sequence is bounded or unbounded?
2)this sequence is monotonic or nonmonotonic
6 Given the sequence an - 3ñ: This sequence is Select an answer v This sequence is Select an answer v Does this sequence converge or diverge? Select an answer v If the sequence does converge, to what value? If it diverges, enter DNE Question Help: D Video D Video Submit Question
Sequence (Longest Progressive Sequence) in C language Given a sequence, the objective is to find the longest progressive sequence arranged in ascending order. Detailed descriptions are as: Problem A sequence is said to be progressive if it doesn’t decrease at any point in time. For example 1 1 2 2 is a progressive sequence but 1 2 1 is not a progressive sequence. Let S be the sequence and be represented by L spaced integers Ki, now your task is...