Using the Fundamental Theorem of caleulus ( e'dt) i 1. -sin(a)ee)- cos(r)en(e) 2. - sin(x)e(e) - cos(x)e) 3. cos(r)en(e) 4. e)-ein(),

Q: 1. cosh z= cosh x cos y + i sinh sin y sinh z = sinh x cos y + i cosh x sin y.

A: According to our guidelines we are supposed to answer only one question, since you have asked more…

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: Find a differential equation that corresponds to the given lirection field. Consider differential…

A: Solution :

Q: 1 29. J1+sin z cot z rp- sin z 30. -dr sec z 31.

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Q: en differential equation by using an appropriate substitution. The DE is ho + (x + Vxy) dy = 0 %3D

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: We have to find a linear differential operator that annihilates the given function.  6x − sin(x) +…

Q: Integration of (Sin(x) + Cos(x))e^x is_

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Q: cosh (T– i) = eT cosl - i eT sin 1 + e-" cos 1 + ie- sin 1 - IT 2 e cosl - i eT sin 1 + e" cos 1 +…

A: First option is correct answer. Thankyou!

Q: f(z) = 3 sin I+ 3 cos z, а (-п, и) on

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Q: establish each identity.

A: Given identity 9sec2θ-5tan2θ=5+4sec2θ First from the left-hand side,  9sec2θ-5tan2θ Here use the…

Q: The coefficient of sin'x in the antiderivative of F(x) = cs (use fraction form not decimal

A: This question can be solved using the concept of integration of trigonometric function.

Q: cosi in the form x+iy %3D

A: On solving,we get

Q: 2) Proof that If y = f(x) = = cos x then dx sin x

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Q: Prove the identity. cosh(x) + sinh(x) = e* cosh(x) + sinh(x)

A: The solution of the problem is given in the next step.

Q: 4. | (3t + t) sin(2t) dt

A: Solution: Consider the given integral ; I = ∫3t+t2sin2tdtI = ∫3t sin (2t)dt + ∫t2 sin (2t) dt…

Q: Consider the differential equation where f and g are continuous functions.   (a) What type of…

A: To determine the type of equation obtained when the variable is changed using u = xy in the below…

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: Using appropriate methods to show that 1. 5x2 + 3x dx x(x + 2)2 1 In |a|+ 6 ln |x + 2|+ (x + C. ++2)…

A: As per the company guidelines we can solve first three parts. I hope that the given solution will…

Q: f(x) = {cos x 0<x< n n < x < 2n find its Fourier

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Q: siny dle = (1-x cosy) Cas y

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Q: cosh (T- i) = %3D e cosl i e sin 1 + e- cos 1 + i e- sin 1 e cosl i e sin 1 + e-TI cos 1 ie- sin 1 2…

A: We know formula of coshx in term of exponential form

Q: Se *( — 3х 1-e*}³/² dx -х )3/2

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Q: Prove the pollowing identity.. (sin x t cos L cas x)- sin 2X-CoS T Sin'x + Cosx

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Q: cos x- cos y X, =0, y,=0; sin |x|-sin | y | x, 0, yo=0; B) f (x, y)= %3D %3D r) f (x, y) = %3D %3D…

A: As per bartleby guidelines, for more than one question asked, only one is to be answered. Kindly…

Q: integral ecos(4t) sin(4t) dt

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Q: Using integration by parts, | - | x sin(x²) dx x* cos(x²) dx = k – Then k is?

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Q: cos*(x)dx

A: According to integration reduction formula ∫cosn(x) dx=n-1n∫cosn-2(x) dx+cosn-1(x) sin (x)n . For…

Q: ( 3cos³x-1 To evaluate the integrand can be transformed to 1- sin?x O [(3cosx - sec?x)dx o f3cosx (1…

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Q: Cycloid arch: x = a(0 – sin 0), y = a(1 cos 0) - -

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Q: A)) Q1/ Find Fourier Sine Integral presentation of the function: f(x) = xe-* , x>0

A: The given function is: f(x)=xe-x ,      x&gt;0

Q: Maclaurine’s series of ∫((cos^2(x) dx)

A: To find → Maclaurine's series of ∫ cos2 x dxSolution →                       ∫ cos2x dx = ∫ 1+cos…

Q: ysiny limy-»o (y+siny)²

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Q: Choose ALL possible answer(s) Integrate 1-cos x sin x dx sin x 1-cos x O= 2 In sec x + tan x + C O =…

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Q: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

Q: cos e - sin 0 Find a closet rank-1 approximation in the l² norm to A = %3D sin 0 cos 0

A: Consider the provided question, The l2 norm or Forbenius norm(FN) is the square root of the sum of…

Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Given: h(y)=sin(y+1) At, y=0

Q: (1+siny)[1+sin(-y)]=cos2y

A: Given:

Q: Integration of (sin(x) + cos(x)) e^x is ______________.

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Q: Prove that sinh z = sinh x cos y +i cosh r sin y.

A: To prove, sinh z = sinh x * cos y + i cosh x * sin y

Q: Using Fourier Series D (1) Sin (wot) 2 Siu (wot) Cos(wot) Find

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Q: Table of Standard Differential Coefficients S(x) nx f(x) ナ+ fODEOF f'g-f.g S(x) S(x) rクー ex a*lna a'…

A: We have to solve

Q: sin21/3x cos3 2/

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Q: y = arctan dy Calculate da Type sin(x) for sin(x), cos(x) for cos (2), and so on. Use x^2 for a",…

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Q: Prove the identity.   sinh(x+y) = sinh x cosh y + cosh x sinh y

A: To show that sinhx+y=sinhx coshy+coshx sinhy

Q: sin 0 d) lime tan 0 sin z-cos z + 1 e) lim, 0 3z

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Q: Beta Function 27 dx (*+ 1) Prove that

A: The given problem is to evaluate the given beta function integral.