1) Find the following integals: 14) S(2? -x) dx le) S x* dx la) S x* dx Ic) )치 dr If) Sdx ax ti

Q: Ao/ prove JhaT cosh(2i4ze)= Coshzi coshde + Sinh 2,Sn hze

A: The main objective is to prove that coshz1+z2=coshz1coshz2+sinhz1sinhz2. The following formulae are…

Q: 1 Prove that 3 dx s VI VI

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Q: Evaluate: S (In(2æ – 1) – (5) + 25 ) dx - Limits: [1, 6] Using Trapezoidal, n = 30

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Q: Led xe R be such thad Xn→x, show that %3D

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Q: The value of the double integral 7 1 4xy dy dx is 4

A: ∫46(∫274xydy)dxIntregation wrt y so x will be constant.⇒∫46[4xy22]27dx ⇒∫462x(49-4)⇒∫462x(45)dx

Q: Prove thiat dx Ś (areten()) ) = し 4+X

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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: if M Z- Sin (xy) fined 4 22 y= lint t-1

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

Q: 11. Jlgull sin(2t +) dt %3D e2t-3 4 4. 64e3

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Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

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: Evaluate the integral.

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Q: Find the exact lanth of the 4=1n (sec(x)), Odyct3

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Q: 8 Evaluate the integral dx using the two-point Gaussian quadrature rule. 16+z1 -2

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Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: In 8) * dx Integrate and evaluate the following

A: we have to integrate the following

Q: If u= In x, then 1- (In x)2 dx=?

A: Find your answer below

Q: *Write ascript Ble for tayler polynamial of order 5 foU= LnX near Por where the out put is ycl-15).…

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Q: 3 Evaluate the gwen tri ple in legral. xsiny dy dz dx

A: Order of triple integral dydzdx

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: d) Numerically approximate the integral 2+ cos(2Vx) dx by 3 Simpson's rule with 6 strips

A: Given integral is ∫022+cos2xdx. To evaluate the integral using Simpson's 38 rule. Consider the…

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: 16 9. Evaluate the integral 4 dx.

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Q: Classify the Stries as nbsolurehy linvergen ti Condibinally lonvergent, divergent 18 K Sin

A: First we  recall some definition-1)  p-test for convergence of series ∑k=1∞1(ak±b)p :     A series…

Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x 1+ x²

A: Answer is mentioned below

Q: Consider the following BVP: - 2u 1 1sxs2 dx Using boundary condition u(1)-u(2)-0.

A: Sincei have attempted similar problems, let me solve the given problem step by step....

Q: Solve the following intial value problem. y^(4)=-cosx+8sin2x, y'''(0)=0,y''(0)=y'(0)=1,y(0)=3

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Q: 7 the n ya In Cx? _y?) Do not Equatio InCx-yリ Do not check modificd Laplace

A: This is a problem of partial and Laplace.

Q: 5. Find ffp(x + y)² dx dy, region in Fig. 17.2.12.

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Q: Suppose you Know that tand 3/12. Vsing this infe, de tevmine cuhot quadiantdis in dnd Caliulate…

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Q: 1. Find b such that |(a) In 3. dx is equal to х (Б) 3.

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Q: 1, fund warginal cictribution for h(x) for 2. Fud condhtimal pdf4 t) . Estaati yi/ a) V. Estuate…

A: As per the guideline, 3 subparts can be answered. please repost the remaining subpart. thank you.

Q: If u In x, then 1-(In x)2 dx =?

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Q: 5 Evaluate ſ“ S" r² sin ø drdøde 0,

A: Evaluate: ∫02π∫0π∫05r2sinϕdrdϕdθ

Q: In GL(2, Z,,). det

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Q: Find Z in (1-j5) 2= tanh cos lat5 express in lagarithm Form

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Q: Integrate the following (a) / tan(z)dx (b) Ju 1 dr /ez – 1 In 2

A: Evaluate the Integrals: (a) ∫tan x dx=∫sin xcos x dx Let cos x =t implies -sin x dx =dt , substitute…

Q: Co

A: Given that: The Taylor series for f(x) = ln (x) at c = 3 is ∑k =0∞ ck ( x - 3)k .

Q: 8. The area of the region outside the curve r = 3 - 3 cos 0 and insider = 6 is

A: We have to represent the required area first.

Q: Use the Simpson's 1/3 rule with n = 8 to estimate: cosx

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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: 1 +y = zy" dy dr

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Q: If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

A: I am going to prove the given identity by using integration by parts and then use this identity to…

Q: ven the SRF:Y- BHPXAU Prove that B, Rind B2 estimalors of true fi and Bz are unbiased

A: We need to prove that the  β^0,β1^    are the unbiased estimators of    β0 and β1 In population…

Q: Evaluate the double integral : 9 dy dx 36 – 12 - 12 -36

A: