468 CHAPTER 14 The Fourier Integral end TransforAS sin(x) for -4sx<0 4. f(x)={cos(x) for 0 4 5. S(x)= * for-100 srs100 0 for jx) > 100 10 11

Q: k Show that L{sin kt} = s2 + k2'

A: Solution

Q: cos' x+cos'x dx is sin x+sin'x Q 9. The value of the integral

A: Introduction :

Q: f(x)= (1-cos x)/sinx +(sin x)/(1-cos x) find its integral

A: To find the integral  ∫1-cosxsinx+sinx1-cosxdx

Q: I sin 2x cos 2x + kog log a|+e] Ans. y de Jogx

A: Given,

Q: sin x 2. Find f'(x) if f(x) = 1 - cos x %3D 1 3. Simplify your result in (2) to show that f'(x) %3D…

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Q: Find the derivative of g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: 2. Se* sin(e) dx

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Q: limit x to 0 sin(4t)sec(1000t)/10t

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Q: Prove the Calculus identity sin-(x) + sin-(/1 – x²) 2 x € [0,1], where sin-, denotes the usual real…

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Q: cos(x) sin (2x) lim x X sin(x) – 1

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Q: Given the following differentiation rules The function (x) is continuous and differentiable and not…

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

Q: In(cosh x + sinh x) + In(cosh x – sinh x) = - 1 -1 Leave Question 2.

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Q: S cos ( x^3 ) dx = * sin ( x^3) + c 3x^2 sin (x^3 ) + c - sin (x^3 ) + c - 3x^2 sin ( x^3) + c none…

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Q: The amplitude of F (x) = } sin is %3D 1/2 2 4

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Q: 2xdx – [3y* +(x² - y' )tan y] = 0

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Q: 1 cotx ln sin-x dx 1 2 9. Scot-x In a/s 2

A: Here is the solution:

Q: Question 8 Find f'(a) for f(a) O f'(x) O f'(x) O f'(x) = O f'(x) O f'(x) cos - 1 cos? an cos - cos 2…

A: I am attaching image so that you understand each and every step.

Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (z²x + cosx*)] [4(cash2x-sinh2x)] (16)…

A: Given that, y(x)=∂2∂x∂zz2x+cosx44cosh2x-sinh2x16cos2πxddx(2x2) This can be rewritten as,…

Q: (g) = In(){ f(In(1)sin (3x) dx In (x) = x 4 cos (3) (1">)in (~ = In (x) (1 sin" (2 X (h) f(x) =…

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Q: ۱/۱ оне 3 2 2X-2X+1 3 x³- x² - dx ㅠ T Sin 3x cos 3x dx

A: 1. 2.

Q: Q\Find e* sin(x) dx О ехр (pі) O (1- exp(pi))/2 O 1+ exp(pi) O exp(pi)/2 O 1- exp(pi) O (1+…

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Q: Differentiate. f'(0) f(0) sin(8) 1 + cos(0) 1 + cos (0) cos(0) - sin(0)(-sin()) (1 + cos(8))²

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Q: x2 - 2x + 3, x<0 cos를+2. + 2, COS Evaluate f'(-2) and 4.

A: It is given that,       fx=34x2-2x+3 , x&lt;0cosx2+2 , x≥0 Evaluate f'(-2).