H-4-2. [5 marks] (a) Consider the sequence (2n 1)I and determine whether it is (eventually) (strictly)...
(10 points) Determine whether the sequences are increasing, decreasing, or not monotonic. If increasing, enter 1 as your answer. If decreasing, enter -1 as your answer. If not monotonic, enter 0 as your answer n + 3. an +2 2n +8 Note: In order to get credit for this problem all answers must be correct You have attempted this problem 0 times. You have unlimited attempts remaining. 12 F1O F9 F8 F6 F5 (10 points) Determine whether the sequences are...
Question 2 (12 marks) (a) Consider the sequence with terms 2n35"5 log n n 1,2,3,.. 13 n8n (i) Determine whether ah diverges. If the sequence converges, find its converges or limit. o0 (ii) Determine whether r diverges. Justify your ansv swer an Converges o n-1 (b) Consider the series (2n)! 2 (n!) and determine whether it converges or diverges. Justify your answer IM8 8 Question 2 (12 marks) (a) Consider the sequence with terms 2n35"5 log n n 1,2,3,.. 13...
Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n = 1,2,3,.... an 13 n8n (i) Determine whether {an} converges or diverges. If the sequence converges, find its lmit (ii) Determine whether diverges. Justify your answer an COnverges or n-1 (b) Consider the series (2n)! 2" (n!)? n=1 and determine whether it converges or diverges. Justify your answer Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n...
show all work | 2n-1) 2. Consider the sequence |(n+1)! a) is the sequence monotone increasing or monotone decreasing or neither? b) Find upper and lower bounds for the sequence. c) Does the sequence converge or diverge? (Explain) 3. Determine if the series converges or diverges. If it converges, find its sum. => [-1-] c) Ë ?j? – 1-1 j? +1
4. Consider the sequence {z,.) such that z1-0, z2-1 and æn-telths,Yn (i) Show that (n) is convergent by showing that the subsequence of odd-indexed terms is monotonic increasing and subsequence of even-indexed terms is monotonic decreasing (ii) Find the limit of {%) (Hint: Consider x,-h-i) 4. Consider the sequence {z,.) such that z1-0, z2-1 and æn-telths,Yn (i) Show that (n) is convergent by showing that the subsequence of odd-indexed terms is monotonic increasing and subsequence of even-indexed terms is monotonic...
Question 1 3+cos(n) 2n X Which of the following properties hold for the sequence an for n 2 1? l. Bounded Il. Monotonic IIl. Convergent Selected Answer a. I only a. I only b. Il only c. I and Il only d. I and Ill only e. I, II, and III Remember what these conditions mean: Bounded means all terms of the sequence have to lie within a specific range of values. Monotonic means the sequence is ALWAYS increasing or...
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
Consider a linear time-invariant system with impulse response hin (-1, n o 2, n 1 h[n]--1, n=2 0, otherwise (a) Determine the system frequency response H(e"). Then compute the magnitude and (b) Does the system have a linear phase? Briefly explain your answer. (2 marks) (c) Compute the system output yin] for all values of n if the input r[n] has the form of: phase of H(e (6 marks) 1,n=1 2, n 2 n3, n 3 4, n-4 0, otherwise...
NEED ANSWERS OF PART (f,g,h,j) Problem 2 [21 marks] Consider a firm that uses two inputs. The quantity used of input 1 is denoted by x, and the quantity used of input 2 is denoted by x2. The firm produces and sells one good using the production function f(x1, x2)-4x053x25. The final good is sold at price P $10. The prices of inputs 1 and 2 are w$2 and w2 $3, respectively. The markets for the final good and both...
Question 1 [22 marks] (Chapt ers 2, 3, 4, 5, and 6) Let A e Rn be an (n x n) matrix and be R. Consider the problem 1 (P2) min2+ s.t. xe R" 1Ax-bil2 1 where & > O is fixed and Il IIl denot es the 2-norm. Call g.(x)=l|2 the objective function of problem (P2) 1Ax-bl2 i) [3 marks] Compute the gradient of g, and use it to show that the solution xi of this problem verifies (I+EATA)(x)...