I. (a) Compute g(x) = £ (n2 +n)x”. (b) Compute E (n?+n)/2". Justify your method. n=0...
Do the following series converges or diverges. Justify your answer. (a) sin?(n) n2 n= i M8 M8 nh (b) 22n 221 n=1
(b) I G)(u) and G'(1) = 2+e Ft2): 3gcx1+1α)-x'(x) faf(x) , compute G(1) and G'(1). g(5a)' 2x for 37 Problem 2 For each function below, find the smallest integer n for which f)0 and find fin-(x) or explain why this is not possible. notation: The factorial function is n!n (n -1).(n-2)3.2.1 example: If (x)2+z2-1, then n 5 andf)24.3-2.1 2(41). (a) (x)95 16z +23. (b) f(x) sin(3z). Problem 3 3 is shown to The graph of the tilted ellipse z2 -...
How is the last step done done N-1 3 i⅔n2 e 10 10 N _ n-0 N-1 3 i⅔n2 e 10 10 N _ n-0
a e Octave a a Caleculator to qn i. Calculate the number N equal to the sum of all digits of your SID ii. For the N × N matrix A = (aij) defined as aij-l if i = j, or i + 1 = j, and aij 0 for all other values of (i,j) Compute (A-)x for x ,,1 ER . Compute (A-1)Tx for x = [1, 2, 3, . . . , NIT E RN. . Compute x-A(A-19%...
5. Partitions For each n e Z, let T={(x, y) + R n<I- g < n+1}. Is T = {T, n € Z} a partition of R?? Justify your answer using the definition.
Kila K2 B B Tag K2 Kila i N2 N₂ A 0 K KIB KIB N K N species 1 species 2 (b) (a) Kila K2 B To 7 N₂ ž K2 Kila D E E X с A ܘܠ A 0 Ky K2/B 0 KB K N N (c) (d) In graph (d), in the lower right-hand region (point C), the combined dynamics the equilibrium point and the carrying capacity of species 1. move away from; toward O support;...
If X ~ N(?, ?2), what is the median of X? Justify your answer (this does not have to be a proof). If Y ~ Gamma (?, ?), show that (a) E(Y)-??. (c) V(Y)???2
Subject: Algorithm solve only part 4 and 5 please. need urgent. 1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g), or f E (9)? Prove your answer. 2. Draw the first 3 levels of a recursion tree for the recurrence T(n) 4T(+ n. How many levels does it have? Find a summation for the running time. (Extra Credit: Solve it) 3. Use...
Compute the following limits and justify the calculations: a. limo*(1 (/n))-n sin(x/n) dz. c. limn-Joon sin(x/n)[x(1+x2)]-1 dr. d. limn→00 Jaon( 1 + n2x2)-1 d. (The answer depends on whether a > 0, . limn-oo a = 0, or a < 0, How does this accord with the various convergence theorems?) Compute the following limits and justify the calculations: a. limo*(1 (/n))-n sin(x/n) dz. c. limn-Joon sin(x/n)[x(1+x2)]-1 dr. d. limn→00 Jaon( 1 + n2x2)-1 d. (The answer depends on whether a...
Let XN(0, 1) and Y eX. (X) (a) Find E[Y] and V(Y). (b) Compute the approximate values of E[Y] and V(Y) using E(X)(u)+"()VX) and V((X))b(u)2V(X). Do you expect good approximations? Justify your an- Swer Let XN(0, 1) and Y eX. (X) (a) Find E[Y] and V(Y). (b) Compute the approximate values of E[Y] and V(Y) using E(X)(u)+"()VX) and V((X))b(u)2V(X). Do you expect good approximations? Justify your an- Swer