Calculate (a) r(4)F(3/4)/r(7/4) , (b) Factorial function x"e*dx = n!

Q: allsweCI -5e" dx converges 4x to

A:

Q: 1 dx is convergent True False

A: Definite integration

Q: et Determine if the improper integral dx converges or diverges. (1 - e)2 If it converges, find its…

A:

Q: (b) Find the value of the improper integral dx with infinite interval of integration, if they…

A:

Q: find integral x3 3) S dx /1-x²

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A: 13-x=z-dx=dz∫113-x3dx we need to find.

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A: Consider the following power series with a radius of convergence R > 0. Let

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A: Given that: f(x)=lnx

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A: We have to solve the integral and check it is convergent or not

Q: Is the integral [_(0) ^(5) x/(x² − 16) dx convergent? If so, what does it converge to?

A:

Q: x° e* dx 00

A: Given : ∫-∞0x5exdx

Q: 5) Approximate x²-1|dx with a right-endpoint Riemann sum using four equal subintervals.

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

Q: Determine whether the improper integral diverges or converges. 1 dx e2x + e-2x

A: Evaluate integral,

Q: dx 3) L. Vx+1

A: Given:

Q: (b) Explain why the integral e x'dx is convergent.

A: Improper integral : If f(x) is continuous on [a,∞) , then the improper integral of f over [a,∞) is…

Q: 1. Determine whether the integral given below converges or diverges. dx - x

A:

Q: Use the previous item to determine if the improper integr 2x – x3 | dx (х — 1)2(г2 + 1) converges or…

A: Given that ∫-∞02x-x3x-12x2+1dxSolution…

Q: Explain why the integral e'dx is convergent.

A:

Q: Use integration by parts to prove the reduction formula: п-1 S (In x)"dx = x(ln x)" – n [ (Inx)"-! п

A: 2

Q: dx 4. Determine if the integral converges or diverges. (x – 2)

A: In this question we have determine the integral converges or diverges

Q: In order to determine if the improper integral -dx converges, we might compare it to the power 7 x2…

A: Explanation of the answer is as follows

Q: If X; derive the moment-generating function (mgf) of X?. Ν (μ, σ) :

A: Given X~ N(mu, sigma^2) We want to find the mgf of X^2

Q: What do you mean  by Stirling's Approximation ?

A: Query- What do you mean  by Stirling's Approximation ? Answer-  Stirling's approximation. Stirling's…

Q: 6. The improper integral 1 dx converges to х -5 попe 2 1 4

A: We have to find

Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: 353, Without integrating, determine whether the integral dx converges or diverges by comparing the…

A:

Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

A:

Q: dX Show that Xe* converges/diverges.

A: Given : an  = 1 / x e(x)^2

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A:

Q: Find the absolute maximum and minimum values of ƒ(x) =10x (2 - ln x) on the interval [1, e2 ]

A: The given function is  ,fx=10x2-lnx on interval 1 , e2. To find the absolute maximum and minimum…

Q: 5. Consider the function f(x)=e*, calculate df/dx with finite difference using forward and central…

A: We can solve this using formula of central difference and

Q: ticle at time t assuming that x(0) = -1

A: The eigen vectors are : v1=-31 , v2=-71 The eigen values are : 7 and 5. The initial condition is…

Q: Determine whether the integral is convergent or divergent. *e-1/x dx x2

A:

Q: 5. Express the integral: e- dr in terms of gamma function.

A:

Q: Find f xln(x +1)dx

A: ∫x ln(x+1) dx =∫ddxx22 ln(x+1) dx and by IBP: ∫uv'=uv-∫u'v =x22 ln(x+1)-∫x22ddxln(x+1) dx =x22…

Q: 4- 13 + 6y = 0 dx

A: We have to be find

Q: 1 dx is convergent The integral x1.10

A:

Q: diverges: too e -2 dx 2. Evaluate the integral and state whether it converges or

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Q: .2 x+15 dx Jx* +3 1

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Q: 1 Determine the convergence of the integral | dx. (2 – x)

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Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

A:

Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: sin (nx + 3) f (x) V is convergent point wise to zero function. n- 1 صواب ihi

A: True

Q: integral of C(1-e^(-bt)) with the initial time being 0

A: Let's find.

Q: b) Determine whether the improper integral `1+ sin r -dx 1+x² converges or diverges.

A: Comparison test :  Suppose for x&gt;a  . If converges then also converges . If diverges then…

Q: (b) Explain why the integral e- *x* dx is convergent.

A:

Q: Find 뿐 for the ry – ln(xy) = 1 0 뽈 ㅇ-볼 O 래 ㅇ-픕 following:

A: The given expression is xy-lnxy=1 we have to find dydx use the derivative formulas, ddxx=1…

Q: Determine if the integral x dx To x² – 9 converges ?

A: