Compute the following: remember to show your working. (a) N An if An = (1 – ,n] + (e.g. x E A3 →} < x <3) n=1

Q: A random process is defined as Y (t) X (t)- X (-a), where X t) is a WSS process and a>0 is a…

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Q: Find the antiderivative of: x*+1 (n+ 1)2 [(n + 1) In x – 1] if n± -1 x* In x dx = z (In x)² + c if n…

A: Find the anti derivative.

Q: dt converges. There is no value of r such that (3t)-" 14.

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Q: Locate the positive root of f(x)= sin(x) + cos(1+x²)-1 using bisection method with initial guesses…

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Q: 1+e-* Show that dr diverges.

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Q: Find the critical number(s) of f(x) = sin x + cos(x) on the interval [0, 27].

A: i have solved question1 for next question please repost.

Q: 3. Recall that x - Poisson(0) = Mz(t) = e"(e*-1). %3D A. Derive the MGF of Z = (F - 0)/ /0/n where F…

A: Please find the solution below. Thank you.

Q: 1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

A: As per our guidelines, we are supposed to solve only one question.  Kindly post other questions  as…

Q: Q11 Determine all the critical points for the following- S(x) = sin'x- cosx On the interval (0, 2n).

A: Given , f (x) = sin2x - cos x  (.) Definition :  Then critical point of a…

Q: 3. Find a sequence of step functions vn : [0, 1] → R (n E N) that satisfy o n(t)dt > 0 and So n(t)dt…

A: To find a step function ψn : 0,1→R n∈N

Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

A: The given function is f(t)=(e-3t-e5t)2. Expand the function implies, f(t)=e-6t+e10t-2e2t The Laplace…

Q: Consider the IVP: x" + (x')? + 6tx = 0, x(0) = 3, x'(0) = 4 Using the Euler method with a time step…

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Q: 2. Show that X H→ In x is increasing on (0,0) and that In 1 = 0:

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Q: 3, Re call Eudlid's proof of In finitude * primes! Shouw that T Cx): = 1{ ps X: p-pinae }12 logz…

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Q: 6. The improper integral 1 dx converges to Vx-5 4 2 попе 1

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Q: 2m+1}. Show that using (e) Let x* = j/2m for some m eN and some j e {0,1, Forward Euler with N steps…

A: As per the question we have to use Forward Euler method with total steps N = 2m And then we have to…

Q: The approximation of the root a of the fanction f(x) -* -Sa +9x +3 in the interval (4,6]accurate to…

A: Substitute 4.5 and 4.6 for x in the function fx=x4-5x3+9x+3 and simplify, to get the values of f(x0)…

Q: 5. Use the comparison test to determine if each integral converges or diverges b) 2 2/3-4 a) e-x² dx

A: Solution: 5.a ∫1∞e-x2dx

Q: A ball is thrown upwards then falls back down to the ground. If h(t) represents the height of the…

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Q: Calculate the average power value of X (n) =5cos(n. π /6) + 6 as defined in discrete time??  I would…

A: This question is about application of powers in signals

Q: Find the domain at the Furetion Iこ1パー25 rate in intervul Notation x4

A: Given f(x)=x2-25x4we have to find the domain of the given function

Q: 1. Aşağıda verilen serilerin yakınsaklık ya da ıraksaklığını belirleyiniz (Yöntemleri açıklayınız).…

A: As you have asked for only question number c, so I am only giving solution of that.

Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

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Q: Compute y = S V1 -x dx using Monte Carlo Method. The integral is approximately 1.5708

A: Given that y=∫-111-x2dx By using the monte carlo method, Take x=sinu→u=sin-1x, dx=cosudu Then the…

Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: sin(²) En=1 is 18 √n a. 1 b. 12/12 c. Converge d. Diverge d O C O a O b O

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Q: 2. Z=e Iny

A: Given that, z = ex ln y x = ln (u cos v) y = u sin v We have to fin dz/du and dz/dv. Then we get,…

Q: 3. Show that for p> 1 and r E (0, 1), the integral below converge: dt tp

A: by limit convergence test we cab prove this, we have to treat the definite integral as summation…

Q: of Let f(x,y)=tanh-1(x-y) with x=e" and y= usinh (1). Then the value of Ot (u,t) =(4,In 2) is equal…

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Q: 11. Prove the absorption law x +xy=x using the other laws in Table 5.

A: To prove: x+xy=x We use the following identities (1) x=x·1 (2) 1+x=1 (3) xy+z=xy+xz    ( This is…

Q: 9. Let f(x) x In(10) Find the most general antiderivative. F(x)

A: Given data÷ So,we need to find F(x).

Q: 2 Consider the function f(x) - A. 6x + 4x8. f(z) has a critical point at z = Find the value of A: A…

A: The given function is f(x)=-6x2+4x-8 .............................. (1)  Differentiate with respect…

Q: Consider the IVP: x" + (x')² +5tx = 0, x(0) = 2, x'(0) = 3 Using the Euler method with a time step…

A: We apply the Euler's method to find the solution we apply the transformation U'=V and V'=-V^2_5tU,…

Q: 4. Find two values of c in [-4, 4] such that f(c) is equal to the average value of f (x) = 3 cos 2x…

A: To determine c such that f© is equal to the average value of f(x).

Q: Integrate f(x) = 0.5 + 20x + 3x4 from a=0 to b=3, given N=12 by using a) Simpson's 3/8 approximation

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Q: suppose the quantity of a substance, Q, decreases by 6.5% in 10 hours 1. find a formula for the…

A: The decay model is represented by,

Q: per integral test, (-1)" A) Σ B) none of these en (-1)" dz behaves like

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Q: a Find the Orthogonal trajectories of the family of r =; 1+coso

A: we need to find the orthogonal trajectories of the given family of the curve in the polar form.

Q: Find Residues by using Lourent's Series f(²)=3/²2 at Z₂ = FL

A: Given f(z) = zz2 - 1

Q: If fn : R → [0, 0) is a sequence of integrable functions, fn + f a.e. as n → 0, and S fn + 0. Prove…

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Q: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

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Q: 17. Find the values of p for which the integral 3-2, dx converges. 3-2p Орe(-1,1) Op > 1 Op 1 Ops1

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Q: 4. Evaluate the following integral fel e(-²²-25) dt

A: Note:-  ∫ e-x2 dx=π2 erfx +C   Given integral is ∫0∞ e-t2-254t2 dt

Q: 3 Find absolute extrema for fCx) = x°-9x´+15x -3 %3D in terval [o,3] Oへ

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Q: A random process is defined as Y (t) = X (t) - X (i- u), where X (t) is a WSS process and a >0 is a…

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Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

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Q: 2. Integral A e3A dA

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.