Show that the functions 1 dn w(x) dxn (w(x)(1 — x²)^), Pn(x) = n = 0, 1, 2, ... are orthogonal to every polynomial of degree less than n with respect to the inner product (f,g) = f'¹₁ f(x)g(x)w(x)dx, (w(x) > 0).

Q: 2. Evaluate the following integrals. 55% -5 dx 0 5x •[v1+xdx ks

A: "Since, you have asked multiple question, we will solve the first question for you. If you want any…

Q: Consider the initial value problem (x + 4y)y' = 9y with y(6) = b. For which choices of b does the…

A:

Q: Let K = {a, b, c, d, e}. Find, for each part of the question, an example of an object that satisfies…

A: (b) Given vertex set is as follows: K=a, b, c, d, e We are asked to find a 4-colorable graph with…

Q: Problem 8. Find all primes p such that both p − 2 and p + 2 are prime. (Make sure to show that you…

A: Any prime number (in general any number) p can be written in either of the following form:      p =…

Q: Solve for the Laplace transform. 1.e sin2t

A:

Q: 1.9. (—) If a stock declines 20% in one year and rises 23% in the next, is there a net profit? What…

A: The main objective is to check profit or loss on shares based on the market strategy.

Q: 297 N 22% 15° 30° x 286 N

A:

Q: Find the set An U. U={q, r, s, t, u, v, w, x, y} A = {r, w, y} B={s, t, v} C = {s, u, v, x, y}…

A: Given information U=q,r,s,t,u,v,w,x,y A=r,w,y B=s,t,v And C=s,u,v,x,y. We have to find the A∩U. Now,…

Q: Find the sum: 3 5. Check that ³0 (5) (3²) = (²) i=0

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. Let A= Z+Z+, B= {n € z|1 ≤ n ≤ 10} {n Ezl1sns 10} C= {10, 20, 30, 40, 50} Evaluate and falsify…

A:

Q: 8. When log y is graphed as a function of log x, a straight line results. Graph the straight line…

A: Given: The graph of log x as a function of log y is a straight line.  The points are x1,y1=1,20 and…

Q: Solve for x and y (3x5y = 22x+1 +22x-1 (3y5x = 22x+2_22x-2

A:

Q: Are the following statements true or false? If true give a proof, and if false give a…

A: Given that the following statements  a) Consider a continuous function f : (0, 1) → R and a Cauchy…

Q: (3) For the function y = x² + 11x – 12. - (a) Find the derivative of this function and use this to…

A: As per Bartleby rules we have to answer only first 3 sub parts.

Q: Σ1(Vn4 - 1-n3). -

A:

Q: Fill in the blank so that the resulting statement is true. The number of distinct proper subsets of…

A: The question is to find number of proper subsets of a set with n elements.   Proper subset: A proper…

Q: (√5 - 3)(√5 + 3)

A:

Q: In mathematical model of projectile the greatest height attained by the particle is value of y when…

A: The main objective is to check the greatest height attained by particle is occur at given t.

Q: Let x, y, and z be an element of a Ring Prove that x(y-z) = xy - xz

A:

Q: the form Many physical processes, e.g., radioactive decay, are governed by an ODE of u' (t) =…

A:

Q: A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least…

A:

Q: Problem 6 Find all sets A, B and C which satisfy the following. A= (1, IB, IC} B = {2,|A|, |C|} C =…

A:

Q: A method for solving first order differential equation 2 5 1 3 4 t 6 Across 4 A differential…

A: 1. Homogeneous 2.complimentary function (function) 3. Variable separable form (separable) 4.…

Q: Graph the following function and then find the specified limits. When necessary, state that the…

A:

Q: Find lim (x, y)→(0,0) x² + 4xy² y² 2 2 if it exists.

A:

Q: 6. Give a combinatorial proof that the identity below for falling factorials holds for all x, y € R.…

A:

Q: Given the following matrices, find the determinant: [3 -2 5 1 [2 1-3 01 0 4 1 4-2 2 3 1 5 a.) AB = A…

A: What is Minor and Cofactor: Each element of a matrix can have its minors and cofactors calculated.…

Q: · Let tn be Let en be Prove That tn = nen the number the number of labeled trees of labelled…

A:

Q: 3. Solve the initial value problem and figure out its interval of validity dy with y(1) = 0. d.x I -…

A:

Q: Newton's law of cooling the rate of temperature of body is proportional to difference between the…

A: The main objective is to explain the relationship between the rate of change of temperature and the…

Q: Problem 5. The following matrix is the augmented matrix of a system of linear equations in variables…

A:

Q: A metal bar at a temperature 100F0 is placed in room at constant temperature 0 Fº if after 20…

A: Given: At room temperature 0°F a metal bar of 100°F is placed. After 20 minutes the temperature of…

Q: NSTRUCTION: Find the standard form of the equation of the parabola which satisfies the given…

A: To Find: The standard form of parabolas: (1) y2+16x+2y+49=0. (2)  x2-4x-8y-28=0. (3) With  Focus at…

Q: Given the functions f(t) and g(t), f(t) = 12 cos(200t + 45°) g(t) = 5 sin(200t + 102°) Solve the…

A:

Q: Let A be an m x m matrix partitioned as A = rank (A) = rank (A₁1) = m₁. 1.2.1 Show that A22 =…

A:

Q: Find the sum 3 1. Σ=o (3) 2. 3. 4 Σ=0 (4) .k=0 -5 Στο (5) .k=0

A: 1 We have to find the sum of ∑k=033k. We know that nr=n!r!n−r!…

Q: Between any two real roots of the equation e* sin x-1=0, the equation e* cos x+1=0 has (a) at least…

A: Between any two real roots there is a one root of its derivative.

Q: You own a motel with 45 rooms and have a pricing structure that encourages rentals of rooms in…

A: We will find a relation between number of room rented and rent collected . Using which we can get…

Q: Let f(x) = ï³, and let z → 8, and suppose that ε =.001. Determine & so that if |z − a < 8, then…

A: What is Limit of a Function: The concept of a function's limit, which describes how a function…

Q: Simplify the sums: 1. ΣΞ,(i + 1) + Σ(1-1)

A: We will use the results:  2 + 2 + 2 + ... + 2 (n times) 2(1 + 1 + 1 + ... + 1) (n times) = 2 * n =…

Q: Power Special Function Name y = x4 y = x5 y = x6 Quartic Quintic Sextic Graph 128 160 96 64 -20 32…

A:

Q: Problem 7. Given that a | (b+c) and gcd (b, c) = 1, show that gcd (a, b) = 1 and gcd (a, c) = 1.

A:

Q: Prove Theorem 1.9 from Theorems 1.7 and 1.8. Theorem 1.9 If f(x,y) has continuous first and second…

A: To Prove: f(x,y)=f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)+R2(x,y), using theorem 1.7 and theorem 1.8 (given…

Q: 7. Let gadu to coins A = | -1/2 1 diens to a 2 Compute A² and A³. What will A" turn out to be?

A: Given, A=12-12-1212

Q: A palindromic number is a natural number whose value does not change if its digits are reversed.…

A: Here we have to find 22 belongs to which region.

Q: Problem 2. Interpret each equation of the following system as a line in the plane. Graph the lines…

A:

Q: The Impulse Response of a System is found to be t^e²t find the Transfer Function G(s).

A:

Q: 1. Find the Inverse Laplace of F(s) = s+4 s²+8s+41

A:

Q: Throughout this question, take care to explain your reasoning carefully. You should round your…

A:

Q: 1. Page 10, 1.2.6*. Show that the following sequences of sets, {Ck), are non-decreasing or…

A: