If the sequence {gm} is orthonormal on [a,b] with weight function w(x), then the sequence {Vw (x) gn(x)} is orthonormal with unit weight function.

Q: Let f(x) = find f(") (x). 2z O a. (-1)"i"(n+2)! O b. (n+2)! Oc. (-1)"(n+2)! 6z13 O d. (-1)"(n+2)! O…

A: The given function is  f(x) = 12x3

Q: (15) (+) The set of all positive integers is partitioned into several arithmetic progressions. Show…

A: (These are 3 different questions. According to our policy, we are just suppose to answer the first…

Q: 1) Given f(x)=2x + 1 and g (x)= x^2 +2x-1 , find (f- g)(x), then evaluate the sum when x=3 2)Given…

A: Given:1. fx=2x+1, gx=x2+2x-1f-gx when x=32.fx=x2, gx=1-xf-gx when x=23.fx=x+2, gx=x-1f-gx when…

Q: Show that the identity k n = n 72 n k k-1, olds for all integers 1 <k<n and use it to prove that n…

A:

Q: Find all the of the polynomial function f (x) = x° - x - 1 at ro = 1.5 at 5th iteration using…

A:

Q: Prove: For any positive integer n, x™1 - yl = (x- y) xy' (You may use the laws | of exponent in your…

A:

Q: let F(x)=f(f(x)) and G(x)=(F(x))^2  You also know that f(5)=10 , f(10)=3,  f prime of 10 = 4, f…

A: The objective of the question is to find the derivative of the functions F(x) and G(x) at x = 5. We…

Q: Consider the quadratic function : C→C defined by f(3) = ² + i. (a) What is the long term behavior…

A: Given : A quadratic equation f:ℂ→ℂ defined by f(z)=z2+i. To find : (a) The long term behavior for…

Q: For any positive integer n, prove that summation d divides n t(d)^(3) = ( summation d divides n t(d)…

A:

Q: (0 < * < 1) (-1<* < 0) (4) If f(x) = %3D expand f(x) in the form c,P,(x).

A: Give that: f(x)=-12, -1&lt;x&lt;012,0&lt;x&lt;1  Here L=(1+1)/2=1 Fourier  series expansion given by…

Q: Prove that x ∈ E' iff there exists a sequence (xn) in E\{x} such that xn -> x.

A:

Q: Prove that the sequence {f(1/n)} has a limit if |f'(x)| < 1 for all r € (0, 1]. I

A:

Q: 1. Suppose that X ~ B(10, 0.12). Calculate: (b) P(X= 6) (е) Е(X) (а) Р(Х — 3) (d) P(X>7) (c) P(X<2)…

A: As per our guidelines we are suppose to answerthree sub parts.Given,A random variable X~B(10 ,…

Q: let F(x)=f(x^7) and G(x)=(f(x))^7  You also know that a^6=12 , f(a)=3,  f prime of a = 11, f prime…

A: The objective of this question is to find the derivatives of the functions F(x) and G(x) at the…

Q: Theorem 72. (Products of two convergent sequences) Let {px} be a sequence that converges to x and…

A:

Q: Let (an) be a sequence of real numbers that diverges to +∞, and let (bn) be bounded. Prove that lim…

A:

Q: The equation x² + ax + b 0, has two real roots a and B. Show that the iteration (i) Xk+1 = - (axk +…

A:

Q: Let f(x) = r sin(1/x) be a real-valued function. Notice that one has -z 0, thenm= sin(z) O E. lim,…

A: We will find out the required value.

Q: 2) The purpose of this problem is to give you some practice with the most common application of The…

A:

Q: Let sequence (tn) = (1 , 0 , - 1 , 0 ,1 , 0 ,-1 ....) What is the lim sup (tn) , and lim inf (tn) ?

A:

Q: Consider sequences (– 1)"n (i) Зп — 1 (1) cos T- (ii) n2+ 3n (iii) Зп2+ 5 n Which of the following…

A:

Q: The Taylor polynomial of degree 100 for the function ƒ about x = 3 is given by (x – 3)100 50! 2n…

A:

Q: x*+1 c. lim X+00 Vx+x-1 Vi+3x4 d). lim 2x+7 Vi+3x e). lim X-o 2x+7 f). lim (v4x² + 3x – 2x)

A: *As per bartleby guidelines we are allowed to answer only 3 sub-parts at a time. Kindly please…

Q: Consider the generating function for the sequence of natural numbers: G(x) = x + 2x^2 + 3x^3 + 4x^4…

A:

Q: The logistic function given by f (x) = is a sigmoid (s-shaped) function useful in many 1+e-* areas…

A: (a) Given that a logistic function fx is defined as: fx=11+e-x which is a sigmoid function and given…

Q: Suppose {xn} is a bounded sequence. Define bn where lim inf xn :_(n→∞) = lim inf bn :_(n→∞). Show…

A: It is given that xn is the bounded sequence. bn:=infxk: k⩾n Wherelimn→∞infxn:=limn→∞bn To prove bn…

Q: Show that if (XN) is bounded sequences, theN (XN) Converges if and only if lim sup (X₁) = lim iNf…

A:

Q: Which function is bounded above and below? Of(x) = x² - 4 O f(x) = (x - 3)³ Of(x) = 3e O f(x) = 3 +…

A: We will use end behaviour to find the function are bounded or unbounded.

Q: A function g has domain equal to the positive integers. Furthermore, g(2021)=2/2021 and…

A:

Q: Find the smallest value of n such that f(x) is O(x^n) for each of the following. d) lnx…

A:

Q: et n > 3 and 2 <k< n – 1. Prove the inequality k + + 2 2. n two ways: (a) algebraic proof, and (b)…

A:

Q: let F(x)=f(x^7) and G(x)=(f(x))^7  You also know that a^6=12 , f(1a)=3,  f prime of a = 11, f prime…

A: The objective of this question is to find the derivatives of the functions F(x) and G(x) at the…