Let o e C (RN), heRN - {0}. For te IR', we set (x + th) – (x) (x) = 1- Show that E C (IRN).

Q: For the ODE dy = y² – 3y dt find a(yo) for Yo < 0 O 00 -V3 O V3

A: Answer

Q: dy +y = zy dr

A: Given equation is: xdydx+y=xy3

Q: (a) Suppose X U (0,n), where n is a positive integer X-[X] U (0, 1). (b) Use the result of (a) to…

A: De Moivre's theorem gives an axiom for computing the powers of complex numbers. We first gain some…

Q: 1. Evaluate the following integral: 4 (t2 + 3) cos(5t) dt

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Q: H) 9f zyzec then prove thal nl x=4=Z, (alogen) %3D

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Q: Let fn E D[0, 1]. Suppose that fh g on [0, 1], and lim fn(1/2) exists. For each x E [0, 1], show…

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Q: Solve the Pollowing dellay diffenential on the in te vval [os 2J by the mpth-d of steps. (a) dx =…

A: I have gotten a unsolved integration in that problem so i write as it is

Q: Recall that 1, x >0 d (]xl) dx —1, х<0 x < d Use this result and the chain rule to find (sinx|) for…

A: Here, recall that  -π,-π2 is 3rd quadrant, where sin is -ve-π2,0 is 4th quadrant, where sin is…

Q: Find dy for the following func tion s -니 y=(1+ cos zt)

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Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

Q: Q1) Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3, by using the Chain Rule dt

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Q: A continuous r.v. F(x1= === 2 × -IN 15 X has CDF X Co OBX C1 18X 16 17 **** 18

A: Given: Fx=0            x&lt;012x        0≤x&lt;1k            x≥1

Q: 1 prove that | e -ym dy = mr(m) -ут

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Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: Let SINGLEDFA = { | M is a DFA and for all s e L(M),|s| = 1}. Show that SINGLEDFA is decidable.

A: Detailed explanation mentioned below.

Q: 10. Find the integral| dt. t* +81

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Q: Let f(x, y,2) = x² sin y+y e", where x =t +3,y = ne*-1 and z = In 2t. at t = 1 is: -2 1+2n O -12n…

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Q: Let T : (0 → l defined by T(Xn)) = ( n. (a) Prove that TE B(l, l∞) and ||T|| = 1.

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

Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral:…

A: This question is based on chain rule differentiation and indefinite integral.

Q: 1. Evaluate the following integral: S(t² + 3) cos(5t) dt

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Q: let f(x) = { ax2+x+1 if x is less than or equal to 1                 { bx if x >1   find a and b…

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Q: If the 2n RVs A, and B, are uncorrelated with zero mean and E(A²,) = E(B²,) = %3D o, show that the…

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Q: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

Q: 1. Evaluate the limits. e' cos (t – 4) dt - 4 (а) lim x2 x2 – 4 e2 + 2 (b) lim x00 e2x + 100

A: Solve the following

Q: (b) Prove that sint -dt > 0 t+1 for all a > 0.

A: Given:- ∫0x sintt+1dt &gt;0

Q: 3. Use the IVT to prove that y = x ln x has at least one zero on 2'2

A:

Q: f(x) = In(2 + cos x). -2.125, xk+1 = Ik +0.5, yk = f (xk), k E N To = %3D %3D = 0r

A: The function is fx=ln2+cosx Conditions: x0=-2.125, xk+1=xk+0.5, yk=fxk, k∈ℕ xk+1=xk+0.5…

Q: Express the limit lim E (4 cos (272;) + 6)A¤; [2, 4] over as an integral. n- 00 i=1

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Q: Solve the following non-homogeneous linear ODE of first order dy 2y + dx sin x

A: Given, dydx+2xy=sinxx To solve the above differential equation.

Q: If the moment-generating function of X is a. M(t)=(1–21)"", 1 < ½, Find the p.d.f of X hence use it…

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Q: S°(t² + 3) cos(5t) dt 3

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Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: d tanh¬' (In t) = dt 1(1 – (In t)²)

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Q: Evaluate the following definite integral e-(s-2)t sin(3t) dt. 2 3 (s+3)2 + 4 (s – 2)2 + 9 2. seçenek…

A: Using definition of Laplace transform

Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

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Q: 6. Suppose f(2) is analytic in |2| 1, and f(0) = 1, f(0) = 2, compute: %3D (1) h = fe(s+ 1)2d: (2)…

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Q: . Let Show that, Hence show that •2T F₁(x) = 2/1/² 0 Fn(2) = eix cos ∞ N=-∞ eix cose eine de in Jn…

A: As per the question we are given the sequence of functions Fn(x) in form of a Fourier integral. And…

Q: Let z= 28x + 32xy - 8y , where x(t,s) = cosh (4t) cos (5s) and y(t,s) = sinh (4t) sin (5s). ze at…

A: Here, z=28x2+32xy-8y2

Q: Let f1(x, y) - e cos(5y), f2(x, y) = x² – 25 y². Find Vf, and Vf2, and show that %3D (fv) = 0 for…

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Q: _Suppose w =+, x = cos² t, y = sin? t, z = ; dw Evaluate at t = 3, by using the Chain Rule dt

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Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: Let M, = Z, – Z;-1, Zo = 0, where {Zn, n21} is a martingale. Show that E(M,„Z„-1] = 0

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Q: If J f(x) cos(mx)dx = and f(x) = En=1 cos(n²z) n3+1 then m = O 4 O 25 O 16 0 4 9 O 5 O2 03

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Q: Prove that by Gamma Function eit + e' e-st dt 2 s2 + 1

A: We will find out the required result using Gramma function.

Q: 1- Find dwi dt at the given value for w ==+2,x = cos (1), y = sin (1),z = w =-+ at = 3

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Q: Suppose w=x/y+y/z, where x=e^(4t), y=2+sin⁡(4t), and z=2+cos⁡(3t). A ) Use the chain rule to find…

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Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…

Q: Q1) Suppose w =÷+ ?, x = cos² t, y = sin² t, z = ; Evaluate dw at t = 3, by using the Chain Rule dt

A: