68. Show that the asymptotic representation of the Bessel function Jn (kr) for large kr is Jn (kr) = - | cos (no – kr sin 0) dô ~ COS CoS kr Tkr 2
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A: Formulae used: ddxxn=nxn-1∫cos(ax)dx=sin(ax)a+C∫sin(x)dx=-cos(x)+Csin(0)=0cos(0)=1
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Q: 2. Use the Definition of Residue to show that: dz -ni 3 Jizl=1z² sinh z Where 0 < |z| < T.
A: Image is attached with detailed solution.
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Q: 1 The improper integral Jo 2+4x+13 dx is given by: Select one: None of these O a. O b. lim…
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Q: 2. Use the Definition of Residue to show that: dz -ni Izl=1 z² sinh z 3 Where 0 < |z| < T.
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Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.
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Q: Which of the following is a left Riemann sum approximation of (x²) dx with n subintervals of equal…
A: Definition used- Left-hand Riemann sum - ∫abf(x)dx=…
Q: -Find Fourier Integral for the function: f(x) = {0 x 0 0 <x < 2 1 ans: f(x) = - " sin2w cos(wx) +…
A: Given function fx=0 x<0 or x>01 0<x<2 So we must have fx=0 x<0 or x>21…
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Q: Let f(x) = -cos(x). Compute ộ = coto + C1T1 where to = 1 and 1i = x. %3D Compute the discrete…
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Q: 3. Evaluate the double integral /sin(x+y) dx dy by using Simpson's 1/3-rule with four sub-intervals.
A: I = ∫0π2∫0π2sin x+ydxdy,
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Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D
A: Given w = x2x = sin(r2s)
Q: The approximation of 1 = cos(x+10) dx using composite Simpson's rule with n-3 is: 1.01259 3.25498
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Q: The modified Bessel function 1,(x) has the integral representation 2 16(x) cosh(x sin 0)d0. N Jo Use…
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Q: 2 1 Evaluate the iterated integral: y sin(Tx) dx dy 1 Jo
A: first we integrate the integtal with respect to x therefore integrate with respect to y.
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Q: 12.)Express lim E(3(x;,)² – 5x, + 2)Ax as a definite integral on the interval [0,1]. i=1
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Q: The integral of the given function | sin 9x cos 4x dx is equal. .... 13 cos(5x) — 5 сos(13x) А. + C…
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Q: The Fourier integrals of two continuous functions f (x) and g(x) defined on R are given by 00 f(x) =…
A: The Fourier integrals of two continuous functions fx and gx defined on R, where…
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Q: Evaluate the integral 3 2x cos(xy)dydx 2
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Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)
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Q: 7. Use integration by parts to prove that for any positive integer n, п - 1 Scos | cos"x dx = 1…
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Q: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos
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Q: 6.3.18. Evaluate the integral. using U substitution integrate (cos^2(x)sin^2(x))dx
A: Hello, there are two functions present in the question. As the first function comes along with the…
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A: This question is based on indefinite integral.
Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.
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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
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Q: |1) Use a sine expansion to compute the solution of ( ди д'и at ôx? u(0,t)=u(1,t) = 0,t > 0, u(x,0)…
A: According to the given information, it is required to compute the solution of the given equations.
Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z2 sinh z Where 0 < |z| < T.
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Q: Show that the p.d.f. of Z is given by g1(r) = e-1(+A)cosh(vAx), x > 0, where cosh(2) = }(e² +e=*) is…
A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…
Q: (4z + 5)² tan zy= + dr Cos z
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Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where 0 < |z| < T.
A: Cauchy residue theorem is one of the method to evaluate the integral of analytic functions.…
Q: b- Use Chain Rule to compute w = 2y e* - Inz } əw at x = ln(t² + 1), at (t) equal to (1) for: y =…
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Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…
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Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…
A: Solve the integral √(x2+25)/9x2
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- Compute the a-limit set and the w-limit set of each point in R forthe flux determined by the differential equation x' = : −x(1 + cos² x) in R.Why does the limit as x goes to 0 of cos(1/x) not exist? Can use two different sequences: xn=1/(n*pi), and yn=2/((2n+1)pi) and show that lim cos(1/xn) ≠ lim cos(1/yn).12. Evaluate the triple integral xyz dxdydz for the following limits: z from 0 to y, y from 0 to 4, and x from 0 to1. 17.Find the limit of sin2x/sin3x as x approaches to 0.