Since Cov (X, Y) = E [X, Y] -E [X] E [Y]. Obtain Cov (Yi, BO)

Q: Use this result and the chain rule to find (Isinx|) pr all x € (-T, T),x + 0. dx

A: Given,           ddxsinxWe know that,             The derivative of absolute function is given by…

Q: .rdx dy Prove that (a) (b) (8)

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Q: Integrate counterclockwise around C. (Show the det に+1 20. ‚ C: |z − 1| = 3 - ²-iz + 2

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Q: Prove that cosh-z = In (z + vz? - 1) %3D

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Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: 7 y=tanx show thats y" = -2Siny cosy 1f y=e Snbx show that:

A: Dear Student, according to the Bartleby guidelines, we can answer only first question if multiple…

Q: az əz 1. ax' dy If z = In(e* + e"), show that %3D %3D

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

Q: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

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Q: Let u = cos(4x) and du = e2x dx, then by using IBP, the integral 1 (a) — e²¹ ²² c cos(4x) +2 SC.²2.…

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Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: 21. Prove that lsio rol ylanoti (i) Res (tan z, x/2) – – 1 1-cos z (ii) Res 12

A: The solution is given as

Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: 2² + e4 z lim z 0 22 – e²

A: This is a form of infinity by infinity so we have to apply Lhospital rule that is differentiate both…

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: af af дх ду af az and of. HINT [See Exam Find 24 fx, у, 2) : x² + y2 + z2 af af ду af az %3D

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Q: Let f(x, y, z) = ln(x² + z) + y²e"z – cos(2yz). Find fzya- CoS %3D

A: use partial differentiation for finding the derivative.

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

A: We need to evaluate integral.

Q: Using the substitution u = 2x – 1, prove that - -3 8 dx 1 (2x-1)3 25

A: The given integral is ∫13x(2x-1)3dx Put 2x-1=t⇒2dx=dt when x=1 then t=1 and when x=3 then t=5 So,…

Q: (Superman Versus m ers arrive according uho

A: System 1 Customer arrival rate in a Poisson Process λ Service time  3μ System Capacity…

Q: cancer u alcurate 5th on diagnostic test is 9s 2 those who halse A 'cancer cnd on those wno do not

A: Given that, As the test is 95% accurate for both who have cancer and who don’t, therefore the…

Q: △XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1).  Which of the following can be used to prove…

A: Given △XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1)

Q: If U(x, y) = -e-Y sin x and f(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = Select one: O ey…

A: We have to find V(x, y) i.e.imaginary part of given analytic function,if we have real part is given.

Q: Sm Vx dx

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Q: Use the substitution formula to evaluate the integral. fin-√3/22 c2x dx 1 + e4x 28) 0

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Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: ronskian of the DE : xp(x)y' + 3y = 0 = er² et? et?

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Q: (b) Evaluate the integral fxIn x dx using by parts formula.

A: Answer is:  (x2/2)lnx -x2/4 + C

Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: B. Switch the order of integration: cos (x2) dædy. Just SET UP with the order switched. DO NOT…

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Q: In Exercise 5.8, we derived the fact that 4y1 Y2. 0< yı < 1,0 < y2 < 1, f(y1. y2) = 0. elsewhere.…

A: Compute the marginal density function of y1 using the formula: fy1=∫y2fy1,y2dy2 fy1=∫014y1y2dy2…

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: •1-i Evaluate 4z dz . J3i

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Q: Evaluate the improper intergal dx using the residue 2 (x² + 4)² theorem.

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Q: Evaluate the integral fff, xyzdV,where: E = {(x, y, z)|–1 <x< 1,0< ys 2,1 szs 2}

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Q: Explain Bessel equation and Prove that 2 (i) (ii) In+3X + Jn+5X =÷(n+ 4)Jn+4x 4J"n = Jn-2 – 2Jn +…

A: Definition Bessel's Equation: The differential equation x2d2ydx2+xdydx+x2-n2y=0 where n is a…

Q: The suitable substitution to evaluate the integral [V tan (2x) dx is cos (2x) O u= sec(2x) u =…

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Q: e In (x le) (2- secx dx to be integrable using the formula - se What should be the value of A for u"…

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Q: - [Mesin(2x) dx = esin(2x) + C_then the Mis equal to +C,t

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Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

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Q: that X and Y have joint pdf f(x, y) ={x + 3x^2y if 0 <= x <= 1 and 0 <= y <= 1, 0 otherwise.   (c)…

A: From the given information, Consider, the Joint pdf of X and Y is as follows: fx,y={x+3x2y if…

Q: 1 (aw C. Ifw=f(x.y) and x=1. coso, y=. sino. Prove that

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Q: e){x*,x%,x}on(0,)

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Q: Prove,J w' Sin wx du %3D COSZ 2

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