28. Show that there are 12 pairs of numbers (a1,az) with 0<aj < 4,0 <a2 <6...
float useless(A){ n = A.length; if (n==1) { return A[@]; let A1,A2 be arrays of size n/2 for (i=0; i <= (n/2)-1; i++){ A1[i] = A[i]; A2[i] = A[n/2 + i]; for (i=0; i<=(n/2)-1; i++){ for (j=i+1; j<= (n/2)-1; j++){ if (A1[i] == A2[j]) A2[j] = 0; b1 = useless(A1); b2 = useless (A2); return max(b1,b2); What is the asymptotic upper bound of the code above?
solve 3.44 by strong induction Statement 3.44. Let a = 1, az = 3, and for each natural number greater than 2 define an = an-1 + an-2. Then an < (7/4)" for all natural numbers n. Statement 3.45. Let aj = 1, a2 = 2, a3 = 3, and define an = an-1 + for all 4 Thong on for all incN
Urgent! Please mark all correct answers and find values of a1,a2,a3 and b1,b2,b3. (1 point) The second order equation 3x2y" + 5xy' +(-1x – 1)y = 0 has a regular singular point at x = 0, and therefore has a series solution DO (x) = ± x"+". N=0 The recurrence relation for the coefficients can be written in the form n=1,2,.... C =( ),-1) (The answer is a function of n and r.) The general solution can be written in...
Urgent!!! Please show all the answers and clearly mark them and please show values of a1,a2,a3,a4,a5 and b1-b6. Thank you! (1 point) The second order equation x2y" + xy + (x2 - y = 0 has a regular singular point at x = 0, and therefore has a series solution y(x) = Σ C+*+r N=0 The recurrence relation for the coefficients can be written in the form of C.-2, n = 2,3,.... Ch =( (The answer is a function of...
Urgent!! Please label all the answers and find a1,a2,a3 and b1,b2,b3. (1 point) The second order equation x2y" - (x – ķ) y = 0 has a regular singular point at x = 0, and therefore has a series solutio y(x) = Σ CnN+r n=0 The recurrence relation for the coefficients can be written in the form Cn =( DCn-1, n = 1,2, ..., (The answer is a function of n and r.) The general solution can be written in...
4) Given Variables: L1 : 0.1 H Determine the following: a1 (A/s) : a2 (A) : a3 (A/s) : a4 (A) : a5 (A/s) : a6 (A) : a7 (A/s) : a8 (A) : Find the current i(t) in the circuit, when i(0)-1A and the voltage is as shown in the graph i(t) -att a2 for Os<t<1s for 1s<t<4s for 4 s<t<9s for 9 s <t i(t) ast + a6 8 vs(V) i(t) 1 2 3 5 6789t(s)
Find all integers x, y, 0 < x, y < n, that satisfy each of the following pairs of congruences. If no solutions exist, explain why. (a) x + 5y = 3(mod n), and 4x + y = 1(mod n), for n = 8. (b) 7x + 2y = 3(mod n), and 9x + 4y = 6(mod n), for n=5.
ㆍ 3 (10) Let = Re', z = re (0<r< R) be two complex numbers. Show the following identities hold: R2 2 OO = Re = 1 +2 C-z ΣΑ. R2 - 2rR cos (-0)r2 coS n(-e) n=1
5. Let f,lr)- x *a. Show that {h} converges uniformly to 0 on [0, a] for any a, 0 < a < 1. b. Does {f,) converge uniformly on [0, 1]?
Solve the heat equation 4,0 < x < 3,1 > 0 kou det u(0, 1) = 0, u(3,t) = 0,1 > 0 S2, 0<x< } u(x,0) = { 10, { <x<3 are the eigenfunctions You will need to apply separation of variables to obtain a family of product solutions un(x, t) = x (x)Ty(t) where X of a Sturm-Liouville problem with eigenvalues an (as in Section 12.1). Using the explicit expressions for un(x, t) gives (8,0) = ŠA, n=0 Then...