Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

Q: Sin (n+))x Conv. unif nナノ on Prablem (5) Is the senies

A: The given series is: ∑n=1∞sinn+1xn+1 The given interval is: 0,π

Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: 2. Use Cauchy's Integral formula, Evaluate the following sin42 IZ1= 3. (Z-4)3

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

Q: Evaluate the integral. 7y 1-7y dy

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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.

Q: 7. Evaluate. LL sin z da dy.

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Q: .3 S cos³xVsinx dx

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Q: If xy In(3 sinh( 3x)), then x2y'= %3D Select one: Ox coth( 3x ) - In( 3 sinh(3x)) 09x coth( 3x ) - 3…

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Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: Show Sn+3 diverges by osing 6n +5 the test for divegence 1こV

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Q: Evaluate the indefinite integral S(z -9-dz 를-9z + 듣 +C 4x4 중-9z + + C 222 - 9x + 7lnx³ + C - 7 9x -…

A: First we write each term using exponent

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

Q: Prove that Cosh [m(t-x) Cosh mh 2mL 2mL

A: The given data is: To prove: emx1+e2mL+e-mx1+e-2mL=coshmL-xcoshmL

Q: Prove by mathematical induetion. Ine I+2 +2+2 +2° = 2.

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: Evaluate the integral.

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Q: Evaluate the integral. 7 √49-x² √49-x²-22 49-x² 1 √²-3³ (x² + y² + 2²)1/2 dy dz dx =

A: Solution:-

Q: ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

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Q: Evaluate the Integral / tanh (2x)đx. A @ --n|cosh(2x)| + C B -In|cosh(2x)| + C © 21n|cosh(2x)|+ C D…

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Q: Obtain the general soluti d²y 1. 7- y = 10sin²x

A: Given: d2ydx2-y=10 sin2(x)

Q: Evaluate the integral. 1 cos 2t dt 2 7x/2

A: To evaluate the given integral.

Q: HiW f(x, y) = x +2xy+y² +3x+5y ils Is.5 of (2,-3) (2,-3) al of

A: The detailed solution is as follows below:

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)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: Show that L₁J - dx x² + 2x + 2 = In(√5-2).

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Q: it is unbaised estimated of a Then Show That ta is baised estimated of O2.

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Q: Prove that, cosh-'x = In |x + vx² – 1 for x 2 1 -기/

A: This question is based on Cosine hyperbola.

Q: Suppose Fas satisfies f'cx) = fex). Prove that 3fx)sin(3x) + f'cx)cos (3x) Sfewcos(3x) dx = %3D 10

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Q: The integral of x²Inx with respect to x is; A -(3lnx+1) +C ® (3lnx – 1) +C © 3lnx – 1) +C 3 D -(Inx…

A: Product rule of integration : ∫u.v dx = u∫v dx -∫dudx∫vdxdx dlnxdx = 1x ∫xn dx = xn+1n+1 +C In…

Q: it is unbaised estimated of a Then Show That ta is baised estimated of 02. Theorem:- if

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Q: 6. Find the fized point of flx) [-,1] where', on fa = (동) x-(올)x3

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Q: 4. Show that In sin 6 d0 = – n 2 by applying the mean-value principle to In |1+ z| for |2| <r < 1,…

A: ∫0π2logsin(θ)dθ=12∫0πlogsinθdθ                         =12∫0π2logsin2θdθ…

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z2 sinh z Where 0 < |z| < T.

A: Use the following formulae, to evaluate the given complex integral. Let z0 be a pole of order n,…

Q: 7. | (x² + + 2x) cos x dx

A: Apply the integration by parts in the given integral. Let  u=(x2+2x) ; dv=cosxdxThen,du=2x+2dx ;…

Q: The term r ryis homogenous of degree two. -

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Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: Solve in terms f Bessel's functrom the folowrng (z=) DES?

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Q: Evaluate the improper intergal 1 -00 dx using the residue (x² + 16)3 theorem. 00 2

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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: 2. Use a theorem to find the ff. Zx if yz? + z = 5xy – 1.

A: Find out the zx when function is given as yz2+z=5xy-1 or yz2+z-5xy+1=0

Q: 5) why is x3- 3x +I X +2 Conti nuous (0,00) on where is it discontinuous?

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Q: 3. Gien that F cxy) = s Can servative find putantial -> functin fo Ě a

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Q: Q2-Prove that = va* – x² ify= ()sin () + () va² - x* = va² – x* if y = (;")sin*+ (4) + () Va² - x²

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Q: 3-Expand In [x? sin³ x /vx2 +1]

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Q: Prove that 1- cosh -1 x= In(x+ Vx- -1 1 x+1 2- coth -In x-1 X = - Vi+x? .2 1 3- csch -1 x = In(-+

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Q: d'y on of x

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