43. a. Insin 0 sin 0 In b. In(3x? – 9x) + In Зx fin (ar) – Inb c. 44. a. Insec 0 + Incos e b. In (8x + 4) – 2 Inc c. 3 In V – 1 – In (t + 1)

Q: 37. ; with r = 1 andh = ;: 0, p2 sin¬! V1-h² /r²-h/r2-n? (0,, 33 47-3/3 (0, 0.71)

A: Let's simplify in steps Let's take the numerator first:

Q: Hw. Determine t posdise red nd d. Sinx a x 2 In(X):07, de. os, Xa. 2, 3-tealion by e position fndla)…

A: NOTE:- By bartleby rules, only question (1) is answered

Q: Compute for the value of tanh (1 – i) Iny + 2.13i In 2 + 2.13i 2 In 5 - 4.25i 2 In v2 + 2.13i

A: To Compute: tanh-11-i Concept: 1. tanh-1z=12ln1+z-ln1-z2. lnz=lnr+iθ+2nπwhere,…

Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: Find dy for the following func tion s -니 y=(1+ cos zt)

A:

Q: If r = (3 cosh 2t)i + (3 sinh 2t)j + 6tk and t = In 2 then اخترأحد الخيارات 8. 16 and T= 867 O K =…

A: Curvature   k=32867=0.0369088811995386.

Q: ди k > 0 at Ans. u = e'(A,eka! cosh ax + Bjekai sinh œx) u = e¯'(A2e' u = e"(Azx + B3) k ¯kai 'cos…

A: The given problem is to find the solution for the given partial differential equation in different…

Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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Q: 2. Let f(r, y,z) = In(r² + 2) + ye* – cos(2yz). Find faya- COS

A: see below the answer as per bartleby guideline we have to solve the first question onl

Q: 2. If z = x° In 2.xy, find at 1,-

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Q: 6. If y = In(r+ 1) In z then what is dy/dr? %3D

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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: Example 8.10. Evaluate Sº (ii) Simpson's 1/3 rule, (iii) Simpson's 3/8 rule, dx Jo. 1 + x² by using…

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Q: 9/ Evalaale he fillow inlag rad S sin'z asx dy x CoSx

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: Aşağıdakilerden hangisi (arctan(ok*) 1+e2kx 2dx integralinin sonucudur ? A)…

A:

Q: 2. It Z = e tanly) , wnere x = S"+ t and y=St, find 22 when S=1 and t =0 2t

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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: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

Q: 2- Verify the following identities : [Sinh( u+ v)+ Sinh(u-vl a) Sinhu.Coshv = Coshu.Cosky =-…

A:

Q: O Consider d = - CoSk; yeo) =0,iylo) Reduce he abore initial vaeue problem To be roltera entegral…

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

Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

A:

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: If fufe.- fuave diffa Veubable at'xo eI fuave difle Veubable at Xo eI Pi:I R,ists-n prove O…

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Q: 4. p² –1) cos[cosh (In r)]dr let u= du=

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Q: Hw: Compute y(#/4) With 8-Y=8(siaxt cosx) in Find Ln Kngg kutta 2 4 order

A: To solve the second order ordinary differential equation by Runge-Kutta method, convert it into a…

Q: To prove that 2 dx 1+ (In x)2 + In x+c = 2 In %3D X1 + (In x)2 we use the substitutions U = Inx then…

A:

Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: Let C be the shortest path that connects a to ni and I = fe (sinhz + 1)dz. Then None of these…

A:

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: S 1.Prove that L (coswt) = %3D s2+w2

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Q: 2. %3D be Centered in a batt co,ogo) andradies I 2. frove thet S-273R

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Q: inlyralf Evaluste the +2) ě Snz.dz whre CiI21= 1, by any tw o methode and compone the resalt.

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Q: 1)the f a) 3 cosh z b) 0 c) in d) n -dz by using the residues is equal to

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Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

A:

Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

A:

Q: 6. Which of the followg quti dy (a) de dy (b) de () +2ry- (e) (4) Al of the above

A: It is given that There are four differential equations option.

Q: Evaluate: / (In(2r – 1) – () + 25) da + 25 ) dx | Limits: [1, 6] Using Trapezoidal, n = 30

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Q: 3 Prove Prive that d tin'u e I du

A: As we now the identity tan2(x) +1=sec2(x)

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: if z, = (1 – v31) and zz = (V3 + i) by De Movier's theorem z,z– 4% = 1 (cos( +5 + isin +5)

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Q: vsin ax (02+4)4= sin x is the fun ction with y %3D

A:

Q: 1. Prove: a. csch x In +c %3D b. sech x = 2 Arctan(e*) + c %3D

A: 1. (a). To prove: ∫cschx=lnex-1ex+1+C Proof: We know that, sinhx=ex-e-x2 The left hand side can be…

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

A:

Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

A: Given, u=cos4x and dv=e2xdx. Formula for IBP: ∫udv=uv-∫vdu