If f is the function defined by f(x) = x + cos 2x, then f"(x) = %3D -8sin 2x O -sin 2x sin 2x 8cos 2x 8sin 2r

Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: The function re* sin(8x) is annihilated by the operator

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Q: Determine whether f(x)=sinx+cosx is an odd or even number

A: Given function is f(x)=sinx+ cosx

Q: O t-sin(t)

A: the answer is t-sin(t)  provided the solution below with steps in step2

Q: Find f if f"(x) = 2+ cos(x), f(0) = 2, f(t/2) = -2.

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Q: What is f (=) if f (x) = sin 2x + cos 2x + sec 2x + 8 %3D csc 2x + tan 2x + cot 2x.

A: The given function is fx=sin2x+cos2x +sec2x+csc2x+tan2x+cot2x. To find : the value of function at…

Q: C- Find f' of the following: 1) √2x³-2² + In ² 2) 3xe³r+1 3) sin ¹(³).

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Q: Let f(x) 39 27 O 1 4√3 O-√6 9 3√3 .-1 (²). Then the second derivative at x = -1,f"(-1), equals = COS

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Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: Ssin8 (3z) cos5 (3z) dz

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Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

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Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

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Q: Let F = (cos(5t), sin(3t) , 5t“) and G = (t cos(5t), cos(5t), Find F +G = (5t^4)+sin(3t)+t^4(C

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