If A= B = verify that A(B + C) = AB+ AC. :) 1 If A = 2 and B show that (AB)" =B'AT 4 -1

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

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Q: 4. Show that z = a' Zax if z = e-al cos(x-at) %3D

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Q: If --kr, show that d? dr %3D dt

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Q: 3) Show that the tangent(45°) = 1. Let "u" = 22.5°, use calculator %3D

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Q: 2) Show that the cosine(45°) = V2 * (0.707). Let “u" = 22.5°, use calculator. %3D - 2

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Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

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Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

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Q: 13. the , xydA, where ySxsy?}

A: First I have set the limiting double integral from given information and then solved it .Final…

Q: The integration expression + 4)cos(3ln(x) +4)dx must be transformed into using suitable choice of…

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Q: 12, Show that ()() = (OC)- n-m' %3D 13. Show thet (A)

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Q: Prove az - ae that d az dz

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

A: Cauchy linear differential equation

Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: 2(1-z) Evaluate S S --) dy dx dz

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 9. Prove (1, sin z, cos z} is linearly independent in [0, 2x].

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Q: In ARST (not shown), mZR 45° and mZS 64°. Find m ZT. %3D

A: Given that, In triangle RST, m∠R=45∘ and m∠S=64∘ To find:

Q: A fence is to enclose a rectangular possible from with area of 400 square meters if P(x) is the…

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Q: Verify Young's Theorem z = In(2x + y) -

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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

A: Given: d2ydx2-y=10 sin2(x)

Q: 2.Prove that I (sinwt) : s2+w?

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Q: Which of the following is true? @ Jcos(3x)cos(4x)dx= [ cos(x) + cos(7x) 2 BAll of the above ©…

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Q: Exercise.2 Prove that cos-1 z =- In(z ± Vz? – 1)

A: The given problem is to prove the given inverse complex trigonometric identity. cos-1(z)=1/j…

Q: In R', the point (1, 1, 1) does not belong to the cylinder x + y = 2. Select one: True O False

A: Given problem:- In R³, the point (1, 1, 1) does not belong to the cylinder x² + y² = 2.  True  False

Q: Use linearization to approximate In(1.2).

A: we can use the following formula for approximate calculations: f(x)≈L(x)=f(a)+f′(a)(x−a). where the…

Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: What are the points in an elliptic curve y2=x3+ 12345 x + 23456 (mod 23459) at x=1? Use one of those…

A: As per the question we are given the following modular elliptic curve : y2 = x3 + 12345x + 23456…

Q: Suppose csc(4) = 2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII %3D

A: Given that                                     we have to find value of…

Q: Inand consicr HeLines (tn) venfy Al-5,-6) isapoint of (d) 2) prme Hat (4,)-b de] 3) Cans tract (d1)…

A: Since your question contains multipart, we solve only 1,2,3. If you need any particular question…

Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: Compute Sinh Z c (az - z where C 121-1

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Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: 2. A. If : = sin(3x+2y) , verify that 2 -3 = -6z ax2 B. If f = x³y3 + 2xcosy + y?lnx then show that…

A: x=sin (3x+2y)

Q: Evaluate the integral. sin (8t + 9) -dt. cos (8t +9) sin (8t + 9) dt%3D cos (8t+ 9)

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Q: (x) = 3x +12x+2, %3D ues of a, b and c such that

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Q: FIND dy AMD dy AMD Gint OF

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Q: 19. Find potential function for = (3xy, æ³)

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Q: 10s¯ + 8s + 29 inverse laplace ( (2s 3s + 7)- -

A: We have to find the partial fraction first.

Q: - 2+j= 5 Z153°.435, 3+ j2= V13 Z33°.69, and 1– j2 = /5 2-63°.435 (1 – j2) (-2+ j)(3+ j2) = 1.386…

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Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

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Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: If [ In(ax)dx = 3, then a %3D 1

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Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: Show that lm Casy -1 CoSy-1

A: