Use a cosine Fourier expansion, as u(x,1) = u,(0) +E, (1) cosnx, to solve =e' cos2x in (0,1)×(0,+0), |ĉu (0,1)=( ex (1,1) = 0,1>0, (1) u(x,0) = x,0

Q: If 17e" +8 sin(x) f(x) = (e'3 cos(x)) f'(0) then f(0)

A: In this first we find f'(x) by using derivatives formula I solved complete in 2nd step

Q: 1. f(t) = 5(e^-4t)[cos(10t)] A. (5s – 20) / (s^2 - 8s + 116) B. (s - 4) / (s^2 - 8s + 116) C. 50 /…

A: Laplace transferom of the function

Q: (x) = sin(x) ompute (5) + * (5 ) + x" (;) IT 2

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Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

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Q: Find the order of growth Σ (12 + 1) i=0

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Q: For the line that has the equation X1 + 2X2 = 10, will pass through: %3D O (5,4) (10,1) O (2,4) O…

A: Given that  The equation of a line is x1+2x2=10 To find a point that will pass through the given…

Q: If f(x) = cos(x) +3z³, what is f'(æ)? O f'(x) = sin(x) +3z³ O f'(x) = sin(x)+ 9x² O f'(x) =…

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Q: de cos² 0

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Q: Given 9 (x) = S* t² cos(t)dt use FTC Part 1 to compute g' (x).

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Q: Use a cosine Fourier expansion, as u(x,1) = u,(t)+ 4,(1) cosnx, to solve du ô?u -= e' cos3x in…

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Q: d dx

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Q: Find the function F(x) such that F' (x) = 8x and F(0) = 1 O 1+4x^2 O 4x^2

A: topic- Functions

Q: Suppose f(x) and f'(x) have the following values. -5 -4 -3 -2 -1 f(x) 8 10 15 16 14 f'(x) -2 -3 9 -5…

A: We need to find  out h'(-5).

Q: Confirm that the standard Fourier forward transform of the double-sided decaying exponential signal…

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Q: Let f(1) = (1 + 2x + 2)*

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Q: .3 S(3 – e3*)²dx

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Q: IfI(u) = [log, (1-2u cos x+ u' )dx, then prove that, I(u)+I(-u)-DI(u²).

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Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: (x) = [*cos(t¹) dt, then g'(x) cos(x7) — sin(x7) — sin(77) + sin(x²) cos(77) - cos(x7)

A: Given query is to find the derivative.

Q: Find f'(x). f(x) = = O V 10x - sin²(7x) 1 f'(x) = = 2√/10 - 14cos(7x) 1 f(x) 2√10x - sin² (7x) 10…

A: This question is related to differentiation, We will solve it using given information.

Q: Find f. f"(8) = sin 0 + cos e, f(0) = 1, f'(0) = 2 f(e) =

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Q: Use the Superposition Principle to solve the ODEy′′ − y = x^2 + sin x

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Q: If h (x) = A B sin a ² R csc (x¹ + 1) CSC (t+1)dt for -≤ x ≤, then h'(x) = *< csc (sin³x + 1)…

A: If  for , then to find ..

Q: Solve F'(t) = t+ F(t – u) cos u du, F(0)-= 4. %3D

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Q: Suppose the Fourier transform F(w)=re-lwl, is known. Show that the inverse Fourier transform, viz.,…

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Q: 1)f(x)=sin³ 2x 2)f(x) = 4coshr 3)f(x) )= sinx cos*x 4)f(x) = e*cosx 5)f(x) = 8 Inx %3D

A: image is attached