Theorem 10 Let (a, b] c R and f : [a, b] → R be a function of bounded variation on fa, b). Then f is bounded on [a, b).

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: Let X be a r.v. with p.d. f. ,x = 1,2,3, ... f(x): e.w. The value of a is: N I3

A:

Q: (2c) Prove or disprove the following statement: “ A UBCANB for any A and B "

A:

Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: (Q. +,.) is a subfield of (F = {a + bV5: a, b e Q}, +,.); (F = {a + bv5: a, b e Q}, +,.) is a…

A: A non-empty subset F' of a field F is a subfield of F if F' is closed with respect to the…

Q: (2) If BC À. then P(B| A) P(B) P(A)

A:

Q: Let 4; = {0, i} . Find U4, and N 4. i= 1 | A;. i= 1

A: Given :  Ai =  0 , i    To find :  The union ∪i=1∞ Ai    and the intersection  ∩i=1∞ Ai   .

Q: NCx) = x² - 2x - 5 MQx) = 2x+3 N of M

A:

Q: help.

A:

Q: Let A = {x € Rx > 5 and x 15 and x 8 and x < 12

A: Given:- A=x∈R|x≥5 and x&lt;18 B=x∈R|x≥15 and x≤22 C=x∈R|x&gt;8 and x&lt;12

Q: Let X₁, X₂,..., X be a r.s. from N(,0) and Y₁, Y₂...., be another independent r.s. from m…

A: Solution

Q: H.W 1.: Use Cayley-Hamilton to find 4 -1 A' and A Where A = [2 1 1 0 1 0 11 2 ]

A: Find characteristics polynomial and use caylay hamilton theorem

Q: Prove.

A:

Q: Let a, b, n E Z. Prove: If a|n and b|n with gcd(a, b) = 1, then ab|n. (I

A:

Q: Let P (A) = 0.4 and P (A ∪ B) = 0.6. For what value of P (B) are A and B independent?

A:

Q: S[e²t. √4+e²] dt

A: Evaluation of the indefinite integral, by using substitution method

Q: Find ||v||. v =i - j + k

A: In the dot product of two vectors, we have to multiply the corresponding components of vectors. The…

Q: Let U= {x |x E N and x< 10}. Let A = {x | x EN and x is odd and x< 10}. Let B = {x |x EN and x is…

A:

Q: Solv...: w.

A: Given: w0=w041/4

Q: Let ā= . Find |āà.

A: Here we will find the magnitude of vector a,

Q: Show that |Z × Z|=|N|

A: ℤ represents set of integers ℕ represents set of natural numbers  To show ℤ×ℤ=ℕ We know that|ℕ|=α0…

Q: a PDE from the following- @u =f() Form メソ

A: We eliminate the arbitrary function f from the given equation to form the required partial…

Q: Prove that OfVg.dr = ] (Vfx Vg) · N ds.

A:

Q: Prove the following statement: (VxR) (x 0 ⇒ (y R) (xy = 1))

A:

Q: Let v = (5, 1, 2) and w = (4, –3, 6). Find each of the following: v+ w, v– 3w, || v||, || v – w ||

A: Solution: The objective is to find the required values

Q: if and only if |z| =3 vlgn

A: True

Q: (А - B) - С - (А -C)- (В - C)

A: Introduction :

Q: 2. Let T=

A: Given that, T=22-1-163201 We have to find adjoint T.

Q: Determine if the following statement is true or false. Motivate your answer. If Re(z) > Re(w) and…

A: We have to check whether the statements, "If Rez&gt;Rew and Imz&gt;Imw then z&gt;w" Is true or…

Q: Let A. B C+ Then b.1 AnB c A Ond An B CR

A: Note:- in given problem some points are missing you don't define any relation between R and A, B.…

Q: If a|b, then a|(bc). Direct proof.

A: