1. Show how to explicitly solve the recurrence equation below (that is, do not simply quote the Master theorem). T(n)=7T(n/2)+n2,  T(1) =1 please show the steps clearly

Q: Determine one real root of 2xcos2x – (x – 2) = 0 cn the interval (2, 3)using the Regula-Falsi…

A: Given 2x(cos(2x)) - (x-2)2 = 0  Let f(x)=-(x-2)2 + 2x(cos(2x)

Q: Solve the following equation with master theorem…

A: Master theorem is general method to solve the recurrence relation in divide and conquer algorithm of…

Q: Consider a population that grows according to the recursive rule ��=��-1+25, with initial population…

A: The objective of the question is to find the population at different stages using the given…

Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: 2 31 2. If Ax = b where A = |1 1 2|, find x if Lo 1 2] a) b = [0 _0 o]" b) b = [5 3 –1]" %3D

A:

Q: The exponential form of z = V2+V26 is O 3 ei mi O 3 eimi O 3 e-imi O 9e-imi O 9emi O 3emi O 9 eimi…

A:

Q: We have considered the case of regular deposits at the end of each month. If deposits are made at…

A: Deposit at the end of each month: Time period:  yearAPR: Balance after  deposits

Q: Solve the equation In (x + 2) + In (x – 1) = In (9x – 17) and check your answers (True / False) %3D

A:

Q: 3) Find the non-recursive formula for f (n): f (0) = 6, f (n) = f (n – 1) + 15 for n>1

A: Given f(0) = 6 and f(n) = f(n-1) + 15

Q: 2. Determine one real root of 2xcos2x – (x – 2)² = 0 on the (2,3)using the Regula-Falsi Method. Do…

A: Here -(x-2)2 + 2x(cos(2x)) = 0Let  f(x) = -(x-2)2 + 2x(cos(2x))

Q: f(n)={1 if n is odd; n if n is even  Prove or disprove. f(n) is O(n).

A:

Q: Solve for z.

A: Given,          A figure is shown below :

Q: Example 2.26. Using iteration method, find a root of the equation x³ + x² - 1 = 0 correct to four…

A: We have to find the root of the equation x3+x2-1=0 using iteration method

Q: Newton's Method requires applying the recursion formula: 2n+1= n f'(xn) a) Consider the function…

A:

Q: Example 2.29. Find the smallest root of the equation X X 1-x+ + ... = 0 (21)² (31)² (4!)² (5!)².

A: This is a problem of power series.

Q: finr the exact solution 2*In(4x)=30

A:

Q: The function U is defined as U(n) = 3 + U(n -1), with U(0) = 0.  A. U is defined Iteratively B. U…

A: The correct option is, B. U is defined Recursively    The detailed explanation is as follows below:…

Q: 6 2²{ - 2s-8) 01 02 03 C 4+2 ett

A:

Q: Find F(0) if F (t) == L-! 16 82 (s+4) O 16 O 4 O 2

A:

Q: A coin is tossed repeatedly, and heads turns up with probability p on each toss. Let hn be the…

A:

Q: For the model (1-B)(1-0.2B)X(1-0.5B)a,, find forecasts for one and two steps ahead, nd show that a…

A: Given: Let Xt∧k=1.2 Xt∧k-1-0.2X∧tk-2 ---(1)

Q: Example 9.10. Solve y2 - 4y = n² + n - 1.

A: Please find step by step answer below:

Q: D; Exponential Shifting ,Theorem 2. (D* + 4D+ 4) y- 'o4 e-*

A:

Q: Solve for J -3J+3)<-15

A: Please note that multiplying by a negative number changes the sign of the inequality. We will use…

Q: The square root of a number N is to be obtained by applying the Newton – Raphson iteration to the…

A:

Q: (7) Let X × P(1) and E(-x)=E(5– 5x), then 2 is. (a) 25/26 (b) 26/25 (c) 12/26 (d) 26 (e) None of…

A: Provided information is ; X ~ P(λ) we know that ; Mean of Poisson distribution is given by ; E(X) =…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.