19. 2 In |x – 1| – 4– 2 In |x – 2| – +C

Q: H(x)= In(x+2)

A: our objective is to find x

Q: 4. Find g[h(x)] if g(x) = x² and h(x) = x + 3. %3D O A. x2-- 3 B. x + 6x +9 O C. x + 3x? O D. z + a…

A:

Q: 19. Let f(x) = e*. Then, for all n, %3D f(n) (x) = e* and f(n)(0) = 1 It follows that T„(x) = 1+…

A: We have given;

Q: 14. Consider that * Sof (x)dx = 2 and f'(1) = 3. Find Soxf"(x)dx. %3D 3 O 5 O 1 O 4 O 2

A: We have to find

Q: 1. Show that, if x(t) and x[n] are even, then x(t) = 2 x(t) dt and > x[n] = x[0] + 2 x[n]. n=-k n=1

A: If a function f(x) is an even function then f(-x)=f(x). Since x(t) , x[n] are even functions…

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: Show in detail that E [(X-µ)^n] = 0 for ∀n , where X~N (µ, σ²) and n≥3.

A: It is an important part of statistics. It is widely used.

Q: 8. Given that (2x-x*); 0<x<2, S(x) = ; elsewhere. a) Calculate E(X), E(X²) and E 2- X

A:

Q: 2. f(x) = In 3r on [1,4 with n =5

A:

Q: 62. a. Show that e>1+x for x > 0.

A: We will answer the first question only as those all are different and we don't answer multiple…

Q: ntiderivative. 7x x² -x-2 OB. In x + 1|-In x- 2| + c 14 .7 14 In x +1- x +1 In x-2 x- 2 3 3 14 7 OD.…

A:

Q: 5. Evaluate the integral. x+7 (x-6)(r-2)*a

A:

Q: 3. Prove the Archimedean Property, if x ER. then there exists K E N such that r SK.

A:

Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…

Q: 1. Expand (r+ 1)(x – 2)(x + 3)

A: We will explain this using commutative law and associative law of multiplication.

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

A:

Q: 11. Evaluate the integral. +3 x² + 4

A:

Q: (0.646. 0.5792) | (1.0.3183) (0. 0) (1.0) (2.0) |(1.43, 0) 04 06 08 (0. 0) (2. –0.6366) (1.564.…

A: From the given graphs, f(x)=g'(x) and h(x)=g''(x)because from the graph g(1) has maxima and g(2) has…

Q: Q4/ Let S(x)=- x-1 S(x)= and g(x)=1+ Find (g(x) and ag)(x).

A: We define two functions: f(x) = x/(x - 1)  g(x) = 1 + 1/x = (x + 1)/x Then, we have to find the…

Q: prove that var (XY) == 0} 03+ 2} · o3+ 13.03

A:

Q: 5.7.4. Show that the two formulas (r = y) and (S(r) = Š(y)) in N.

A: Hi, since there are 2 questions given, the first one is answered.  Given - The formula  x=y To prove…

Q: π/2 The integral f/2 fossin drde is equal to O-1/2 O 1/2 01 00 10

A: We have to find the integral ∫0π2∫cosθ1sinθ drdθ .

Q: Show that g(t) = t2tant takes on the value ½ for some t in [ 0 , π/4 ].

A: gt=t2tant on the interval 0, π4. When t=0, g0=02tan0=0 When t=π4, gπ4=π42tanπ4=π2161=π216=0.6168

Q: X = {a,63 wiTe tind large To Pology le T 2) on X

A: There are 4 topology based on above given set elements Discussed below

Q: Consider the following LP Min z = 3x, + 2.x, +7x, s.t - x, + X, =10 -2x, + x, - x, <-10 *,X,,x, 2 0…

A: Hi! As per norms, we will be answering the first question. If you need an answer to others then…

Q: (5) Show that T(n)o(n) > n for all n E N. 11

A:

Q: 28. (a) Prove that for x e R" and s < t, Ds(x) C D;(x).

A: The notation Dsx represent  an open ball of radius s, centered at x∈ℝn. Let x=x1, x2, …, xn,…

Q: dx = In|x| +C^O .BO In|x - 1|+C ® O 5ln|x|+C°O 5In|x-1|+CDO

A:

Q: Let X~N (6,2) and P(X>a)= 0,3 Find a?

A: GivenX~N(6,2)Mean(μ)=6standard deviation(σ)=2

Q: (b) Pr[X > 0.6n] < 0.85. Let X be the number of HEADS after n fair coin tosses. Show that

A:

Q: ν4-x (h) N(x)=; In|x|–1

A:

Q: p(x) = (e³x+5 + n)³. q(x) = In(5e* + 6 tan x). u(x) = e*In(x)-x+2.

A:

Q: 2.4.10 Show that det(e4) = etr(A) for all A E Mn(C). D %3D

A: The given problem is to show the given identity. To show: det(eA)=etr(A) for all A belongs to Mn(C).

Q: 20 + 7)* Evaluate the integral dæ + 7)* * by making the appropriate substitution: u = dx (2x + 7)4

A: Let's find integration of given function.

Q: 3 If [E dx = In(7x - 6) - +C, find f (1). 7x - 6 Enter an integer or a fully reduced fraction such…

A: Given that:-∫f(x)xdx = ln(7x-6)-37x-6+CTo find: value of f(1)

Q: 3. Suppose that the pmf of X is x-1 1. p(x) ,t = 1,2, 3, . 3 3 Find the mgf of X.

A:

Q: Show that for any n E N, n(n + 1)(2n + 1) %3D k=0

A:

Q: J o とツ(x)心 り(- ニ 2) n (x) +In (5+x) = 2 Ino 3)\oy (メ-7) 2 5

A: Simplify the given expressions

Q: S f(x) = x² – 2x + 6 x > 1 x4 + 2.x3 + 2 x <1 Show that there c E (-2,3) such that f(c) = 4. (Don't…

A: topic - continuity and limits

Q: QUESTION 11 Determine whether y or y and x y= Sx4+6x 2 -s y as x- y as x Oy as x y as x y as x y as…

A:

Q: S (In x)²dx A x (In x)² + 2x In x + C C x (In x)² – 2x In x+ C в x (In x)² + 2x In x + 2x + C x (In…

A: Let,I=∫lnx2dxI=∫1*lnx2dxApply integraion by…

Q: x is within 5 units of 1. Olx-1 s5 |x - 1|> 5 |x -1|2 5 Olx-11-5

A: We will solve the problem

Q: 16 Find F(0) if F (t) = L-} O 4 O 2 O 16

A:

Q: (27) Let X = P(2) and E(-x) = E(5 – 5x) find 2.

A: Given: A random variable X follows Poisson distribution Mathematically, X~Poi(λ) The probability…

Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: 4/5elve R(X)= X-2X-5 Using secant e thed, Cerreet apto 2 decimal plases.

A:

Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

A:

Q: 4. Prove that n(3n – 1)r x + 4x + 7x + ... + (3п - 2)x for n e N.

A: