Fn is even if and only if 3|n.

Q: [1] The forward-difference formula can be expressed as h h2 f'(xo) = [f (xo+ h) – f(xo)] f"(xo) f"…

A: Consider the provided question, The forward difference formula is given as,

Q: Determine all values of x so that det(A) = 0, where A =

A: Given: The matrix A is x12x. Calculation: The determinant of the matrix x12x can be obtained as,…

Q: e3x e(n+1)x = 1+ e" + 2 enx Sx 6. n! (n + 1)!

A:

Q: If f(x) = 5³x then f'(x) = 5.A 5h 3 In S O 3x(5³-1) 5³ (In 125) 3(5²)

A: Here, the given function is: f(x)=53x So, note that ddx(ax)=axln(a) where a is a constant.

Q: Show that if x > 9, then x³ – 8x? + 2x > 3. Show that for all n e N, if n > 10, then nª – 2n² > 3n³.

A:

Q: For any n e N, let An = {x € R | –n <x < n}. Prove that NneN An = A1. (Recall that we define 0 ¢ N.)

A:

Q: Let n 2 2. Assume that Fn is prime. show that Fn = -1.

A:

Q: let X1, X2, ..... XN Find UMVUE for 0² N(0,1) 0 € (-∞0,00)

A: Dear student, If you find this solution helpful please upvote ? it.

Q: (3) Let if x 2 Evaluate each of the following, if it exists.

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the value(s) of such that х -1 2х 1 -1 0=12 2 -1 -x O x=4 or x= -3 O x= -4 or x = -3 O x= -4 or…

A:

Q: Show that for all x, e* > 1 +x.

A: It is given that, ex≥1+xwe have to show that for all x.

Q: Show that S1 = S2 if and only if Si U S2 = S1 N S2.

A:

Q: If n is any real number and f(x) = x", then f'(x) = nx"-!

A: Why does ddxxn=nxn-1                 ddxfx=limh→0fx+h-fxh…

Q: Let a, b eR with a < b. Assume that a + <b - for all n E N. Show that b- = (a, b). %3D n n=1

A: We will show  two sets are equal.

Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

A:

Q: A. If X~N(196,20), find x such that Pr(X < x) = 0.945.

A:

Q: Let, a, = 3, a2= 4 and for n2 3, a,= 2an-1+ an-2, express a, in terms of n. %3D

A: we have the nth term of A.P is given by  an=a+n-1d here,  a=3, d=4-3=1an=3+n-11=2+n we get,…

Q: Show that 1-r for any r 1 1 and any 3. nEN

A: answer

Q: f x and y are two positive real numbers, then there exists a positive integer n such that ny>x

A:

Q: by xRy if and only if 7 divides x² – yʻ.

A: A relation is equivalence if it is reflexive,symmetric and transitive

Q: 2. Let, a1 = 3 and for n > 2, an 2an-1+1, express an in terms of n.

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: d x" = nx"-1 de 4. Prove that NɛQ

A: ddxxn=nxn-1 ;   n∈Q

Q: for all integers n >1 E, i = n(n+1} %3D 2

A: To prove the sum of n natural numbers n≥1 is  ∑i=1ni=n(n+1)2

Q: Prove f:N - N. F(X) = 5x is injoctive.

A:

Q: Let S= {n | n=5 k+ 4 for some integer k} Let T= {n|n=5 j– 1 for some integer j}

A:

Q: Determine all values of x so that det(A) = 0, where

A: Determine all values of x so that det(A) = 0.

Q: -a = Y express L and K as expressions of

A:

Q: If F(s) : then (s-1)² '

A: This question is related to Laplace transform

Q: Let g(x) = { x-3 3-x |x| -2 if x50 if 0<x< 4 if 4 Sx Find a number x such that g(x) = -4 o 7 o 4

A:

Q: Derive a formula for fx* In x dxwhere a.) n+ -1 b.) n = -1

A:

Q: Show that E-o (-1)*(")=0, and then verify that () + C) + C)+ - = (") +C) + () +-- -G) + G) + G)-…

A: We can show given identity by definition of Binomial theorem:

Q: Let x be defined as x = x² -x + 1 for all values of x. If p = p -3, what is the value of p? A 1 BO…

A:

Q: let N= 1007276145 and f(x) = e^(x−1)(b − x). 1. Find f'(x), f^2(x), and f^3(x). 2. Find b such…

A: Given: fx=ex-1b-x Using product rule of differentiation (fg'x=f'xgx+fxg'x ) , we get…

Q: The function f(n) = 0.0007n² + 1000n +5 is O O(nlogn) O O(n) O 0(1) O O(n²)

A: Here, f(n) = 0.0007 n^2 + 1000 n + 5

Q: Let n be a positive integer, then n+1≥ for all n.T/F

A: We need to show that n+1≥n for all n where n is a positive integer. Lets proof by contradiction

Q: Prove the following: a) Show that ||ū + ở|| < ||ū|| + ||7||. b) Show that ||ū x 3||² = (ū ·ū)(³ · 7)…

A:

Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: Prove that if f (n) ∼ A(n) as n→∞, then A(n) ∼ f (n). 2. Prove that if f (n) ≤ g(n) ≤ h(n) and f (n)…

A: Given that, fn≤gn≤hn and fn~An and hn~An We have to prove that, gn~An

Q: Let X~N(3,0²). Suppose that P(3<X<6)=0.4 · find P(X<0) ?

A: Given: X~N3, σ2 and P3&lt;X&lt;6=0.4.

Q: If X~N(0,1) then X2~

A: In question,  Given that X~N(0,1). Then we'll find the distribution of X2. he solution is below,

Q: 2. Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 + 5n, express an in terms of n.

A:

Q: Let f (x) = -2r, de fined on -1, 1], then L (P ) = 2 (n– 1) 2- 4 (n+1) 4 (n – 1) 4 (п-1) 2n2

A: We need to find the lower Riemann sum

Q: Prove that the value of the expression (а — 1)(а — 3)(а — 4)(а — 6) + 10 is positive for every a E…

A: The critical points for the function are the set of values where the function attains its maximum…

Q: Let a, b e R with a < b. Assume that a + <b - for all n E N. Show that 1 = (a, b). a + ,b n n=1

A:

Q: (b) Z/n = (q) if and only if kq 0 for all 1 < k <n.

A:

Q: If the statement is true, prove. If the statement is false, disprove. 1 + 2" > 3n for all n E Z

A: False.  take n =2

Q: Let f(n) = n³ + 3n – 4 and g(n) = n³. Prove that f=O(g) and g=0(f).

A: f(n) = O(g(n)) means there exists some constant c such that f(n) ≤ c · g(n), for large enough n…

Q: h >x hɛIA

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.