Show that z- sinh z Rcs :* sinh z

Q: of cosx = = sin(x + 4 €) by Perturbation method. Find root over = of cosx =

A: As per the question we are given a perturbed equation as : cos(x) = ε sin(x + 4ε) And we have to…

Q: Find the solution to the differential equotion that Sotisies the quen inital condiion

A: The differential equation with initial condition is given as

Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: Find dy Sinx

A: See the details solution in below

Q: Find hale reange Sine series Ex 2 (odd fourier sseries) For the function

A: Given function is: f(x)=x, 0<x<π2π2, π2<x<π Here, L=π f(x)=∑n=1∞bnsin(nx), where…

Q: Differentiate. cosx² + siny³ = 36 %3D

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Q: Approximate the sol of x = sinx upto 4 decimal places by using Newtons method.

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Q: Evaluate the integration 2.5 o cos(x) with h=0.5 by using 3/8 Simpson Rule. Write your answer in 4…

A: The Simpson's 3/8 rule states,∫ydx=3h8y0+2y3+y6+ . . . + yn-3+3y1+y2+y4+y5+ . . . +yn-2+yn-1+ynWe…

Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

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Q: Directon. tanx 6. Oy= (sinx) Fan a ANS: AN

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Q: What is the integrable form of sin-cos-sin@ de? 2 2 sinu du cosu du

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Q: @Hiw/ prove that cosiz=coshz @ Cosh'z -sinh'z=1 @1-Tanhz Sechz D cos hiz-l = cschz COS 3 =- Sinh z…

A: (2) we have to prove that,                                                      cosiz=coshz we know…

Q: Integral of Sin^2(2t)cos^2(2t)dt

A: Given: ∫sin22tcos22tdt

Q: to tal differential of eind the the り23 function ] 2=e + tan Z= Sin 2.

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Q: find show that Q Coshz =CoshX Cosy+isin hx Siny

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Q: use the Mean value Theorem to establish Isine-siny </2-y) Ve,yER

A: We will prove the inequality as following.

Q: One solution of a 2nd order homogenous LDE is e2*sinx. What is its general solution?

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Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

A: Given that: y=Acosx+Bsinx

Q: lim 3 2y ソ→o ソーSiny -sin.

A:

Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

Q: (у — siny)(y'сosx — cscy) :

A: Solve the differential equation                          (y'-siny)(y'cosx-cscy)=0

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: Given: 4 2 y = -arctan sinh 3 х — find y' at x = 2 - cosh 1 - y 1 + sinh? 1 %3D cosh 1 y = 1 + sinh…

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Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: find: de So 2-cose using sediment theorem

A: Solution :-

Q: 2 Find def differentiêt equatcn of: -I(082 Siny %3D

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Q: If Z= sinh () show that: *=+y==0

A: GivenZ=sinhyx

Q: zy (Smxa CosX) Axー Sinhy

A:

Q: vx +1 Sinh Cschx = In 671 %3D %3D

A: First, let us evaluate sinh-1x.  Let  sinh-1x=zx=sinhz It is known that sinhx=ex-e-x2 Therefore,…

Q: Consider sin¹x cos³x dx. If we let u= sinx, the integrand can be transformed to

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Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

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Q: Evaluate the double integral [ Vy sin ydydx.

A: • Here, the inner integral w.r.t 'y' is difficult to evaluate, hence we have to change the order of…

Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy %3D

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Q: If Z= sinh () x- show that:

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Q: TRC Prove that CoshZ =Goshx Cosytrisinh X Siny

A: The given problem is to prove the following complex hyperbolic trigonometric identity.

Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Show that coshr+ sinh a = e and cosh r- sinhr = e. Hence, deduce UTMOU cosh r- sinh z = 1.

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Q: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: IT Evaluate the integral: (cos x + sin x cosx)dx

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Q: Integral of cos2x on [0, infinity]

A: We have to use limits to find the given integral.

Q: Prove that cosh(x±y) = cosh x cosh y± sinh x sinh y.

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Q: Find the product of the integral ri sec²(cos(x))dxdy sin-y

A: Given ∫01∫sin-1yπ2sec2cosxdxdy

Q: prove that cosh(x + y) = coshx coshy + sinhx sinhy

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Q: What is the integrable form of sin 0 sin-cos-sine d@? 2 2 u² – 1 du 1– u² du 2 | cosu du -2 | sinu…

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Q: do sin 0 – cos 0 cos 0

A: The given integral is ∫dθsinθ-cosθ

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

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