The Fourier integral of the function f(x) = } 0, x<- and is given by f(x)~ S (A(a) cos(ax) + B(a)sin (ax)) da

Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

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Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: Let f(x) = 3 cos a - 2 tan a f'(x) = r() - C f'

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Q: Find f. f(0) = = f"(0) = sin(0) + cos(8), f(0) = 3, f'(0) = 2

A: f"θ=sinθ+cosθ Integrating both sides  ∫f" θdθ=∫sinθdθ+∫cosθdθ f'θ=-cosθ+sinθ+C..... (i)  Put θ=0…

Q: 10. | [3 - e-lxl – cos x + log(x²)]dx = 0 x³ +4x – sin x 11. x² – 7 -dx 3 0

A: 10. ∫a53-e-x-cosx+lnx2dxEliminate absolutes =∫a53-e-x-cosx+lnx2dxApply the Sum Rule:…

Q: Determine f'(x) for: Ax) = sin (5x - 2)

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Q: f(x) 3 cos x 2 tan x - - f'(x) = f' 3 r()-

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

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Q: Consider the system a = x1 + x2 a = 4x1 – 3r2 with initial conditions a1(0) = 1 and r2(0) = 2.…

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Q: Consider the function f(x) whose second derivative is f"(x)=5x+3sinx if f(0)=2 and f'(0)=2 what is…

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Q: If j(x) = e(sin(x)+cos(x))² , then j'(x) = 2 cos(2x)el+sin(2«) COS

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Q: If you're faced with a graph where each node has an even degree, how would you go about finding a…

A: Necessity:Let G(V, E) be an Euler graph. Thus G contains an Euler line Z, which is a closed walk.…

Q: Let f(r) = cos(4r + 4). f'(x) =-4 sin(4r -4) f'(2) = | 0

A: Solve the given problem.

Q: Let f(z) = 4 cos I-3 tan z. %3D S(2) =D %3D

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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: The function f(x) = a sin x + b cos x + c satisfies f"(x) = cos x – 2 sin x, f'(0) = f(0) = 2. Find…

A: a=2 b=-1 c=3

Q: Find tanget line to f(X) =tan(X) + 9 cos( X) at X=π

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Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Let f(z) = (9 sin z + 2 cosz)tan¹z

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Q: Determine the concavity of the function f(x) = cos x^2 + sin x^2 + x^2 between x = -1.5 and x = -2.5

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Q: Let f(x) = tan (cos(2æ)) f'(x) = Preview

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Q: Find f. f"(0) = sin(0) + cos(8), f(0) = 5, f'(0) = 2

A: Given, f"(θ)=sinθ+cosθ f(0)=5 and f'(0)=2

Q: Let f(x) = (8 sin z + 2 cos z)tan f'(z) -

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

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Q: f"(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 4 f(0) = -sin (0) - cos(0) + (0) + 2 x

A: Given the ordinary differential equation:.The aim is to find the function f.Integration Formula:

Q: Can you find f

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

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

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Q: Let f(x) = 8 sin r + 3 cos r f'(x)- f(똥) =|

A: The given function is f(x)=8sinx+3cosxTo find f'(x) and f'5π6

Q: 2) Find f' (=), f" (A), f" (E) given f (0) = sin 30 cos 0

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Q: Let f" (x) = 6x - sin x. ƒ' (0) = 1, f(0) = 2. Find f(x) ○ x³ O x³ + sin x + 2 ○ x³ – sin x + 2 ○ x³…

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Q: Find f. f(x) = f"(x) = 5ex - 7 sin(x), f(0) = 3, ( 77 ) = 0 EN 2

A: Given :f''x=5ex-7sinx

Q: Find f. f "(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 3

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Q: (1 point) Approximate cos(4.6) using a quadratic approximat First note that cos(4.6) cos(3/2). Let…

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Q: Let f(x) f'(x) = 2 cos x + 7 tan x 2 sin(x) + 7 sec²(x) 1' (5) = 6

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Q: Let f(x) (3 sin a + 2 cos x)tanx f' (x) =

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