Suppose f(x) =cos ( 3x – 2). Evaluate: A -3sin(3x - 2)+C ® -sin(3x- 2) + C sin(3x – 2) +C 3sin( 3x – 2) +C

Q: 1. Find the convolution of f(t) = 3t and g(t) = sin2t?

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Q: Suppose f(x) = sin 4-x). Evaluate: x) dx (A - 3cos FC B -cos 3 X-4+ C 3 Cos 3 (D) 3cos -x- 4)+C

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Q: If fx*cos x dx = f(x) - j2xsinx dx, then f(x) is A. 2 sin x + 2x cos x+C B. xsin x +C %3! C. 2x cos…

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

Q: (a) Let f(x) = cos(3x – 2). Find f°"(x). (39)

A: According to bartleby guidelines I can only answer one out of the two questions given.

Q: A 61. f(x) = -2 cos (3x); 0 sxs 1/3

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Q: If f(x) = 5 sin x + 12 cos z, then %3D f'(x) = f'(2) =

A: The question has been solved in detail in the next step.

Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 |

A: We will find out the required solution.

Q: Evaluate D(sinx – 4e2) D³(sinx cos x-32 e В -cos x-32e2 C) -sin x-32 e2x (D sin x-32 ex A

A: The objective is to evaluate, D3sinx-4e2x

Q: Evaluate: Sv*+sin/x dx. A x+2cos/x+ C 2x+ cosx B + C 2

A: We have to solve the integral

Q: find ap for f(x) =cos 2 [0,2n]

A: a0=0

Q: Suppose S (x) =sin(3x – 2). Evaluate: /f(x) dr A - 3cos(3x – 2) + C (A) (B ® --cos(3r – 2) + C ©…

A: Given, f(x) = sin3x-2To evaluate:∫f(x) dx This can be done as follows:

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

A: Solve the given problem.

Q: The complementary function of (D² +4) y = 3 cos2x is О CF %3D Сј cos(-2x) + C2 sin(—2х) O CF = C1…

A: We need to find the complementary function . We have the function , D2+4y=3cos(2x)  Writing it in…

Q: Find the function that satisfies the given 4. f'(x) = 2 + cos x and f COS X = 1

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Q: Let f(x) = 2x? cos(4r). %3D f'(x) = - 8x sin(4x) + 4x cos(4x) COS f'(2) = %3D f"(x) =|| 0 f"(2) =| |

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Q: If ¹f [ 2³ sin ædæ = −2³ cos x + 3x² sin æ+ 6x cos a - 6 [ f(x)dæ, then f(x) = a. x cos x b. sin x…

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Q: Use the Substitution Rule to provethat∫cos2ax dx =(x/2) +(sin(2ax)/4a) + C.

A: The given integral is ∫cos2axdx=x2+sin2ax4a+C

Q: Given, f (x, y) = sin (x²y – 2x + 4). Find fy. - x cos (x²y – 2x + 4) x² cos (x²y – 2x + 4) O-x² cos…

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Q: 15. Evaluate f e sin2x cos 2x dx A. 2ecos 2x + C C. 2e sin 2x В. + C 2ecos 2x D. 2esin 2x + C

A: You need to have the idea how to use substitution in integration.

Q: 1. a. Let In = exp (nx) sin (exp (x)) dx. By making an appropriate substitution, or otherwise,…

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Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

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Q: Suppose F(4)=-4, f(x)cos F(x) dz F(5)= 3, and F'(x) = f(x). 3 cos (3) +4 cos(4)

A: We can evaluate the given integral by using the substitution u= F(x).

Q: find the aradients of the functions below a)f(x, y) = e-3y cos4x

A: We have to find

Q: Differentiate the function: y = e-x cos²x x²+x+1

A: To differentiate the function.

Q: O f (x) = -6 sin(3x + 1) cos(3x + 1)ecos"(3+1)

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Q: Evaluate Sin (OS - Cos(2x 2. F(Xg.2)2(24-2)で+(2x)デさ(x-g)K C:F(t) = -3€ t+ (2€ + 1) jt4kg ÖZ t<2

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Q: Evaluate f(e' + cos(30) de 1 [ (x³ + cos(3.x)) dxr x sin (3x) ,. a) 4 r* sin (3x) b) 4 3 3 x* sin…

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Q: Find the function f(x) such that f''(x) = 6x + 3 cos(x), f(0) = 5, and f(1) = 2 − 3 cos(1).

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Q: 3. Determine the exact value of f"(0) for f(x) = (cos5x + 5x²)*.

A: Given

Q: Thus, for u = g(x) = sin(5x), %3! f'(g(x)) = F'(sin(5x)) = 8 %3D %3D 8 Next we calculate g'(x). g(x)…

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Q: find where f'(c)=0 f(x)=-cos4x

A: Given, function

Q: find ao for f(x)=cos 2 [0,2m] .a .b IT .C 2n .d 2

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Q: Evaluate f cos*x sin² xdx. 1 16 A B O A 1 -x+ sin 4x 48 1 =x+ 16 1 8 sin 4x 1 64 1 sin³ 2x + C sin³…

A: We need to evaluate integral.

Q: a) f(x) = cos5x %3D b) g(x) = cos*5x %3D c) h(x) = cos*5x + 3x %3D

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: 12. If f(x)=sin(2x+1), then f'(x) is equal to A -2 cos (2x+1). 2 cos(2.x+1). 4 cos(2x+1). C D -4 cos…

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Q: Evaluate D³(sinx - 4e²x) (A) sin x-32e²x (B) -cos x-32e²x C -sin x-32e²x D cos x-32e²x

A: Finding the third derivative of the function

Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

Q: 4. Find f'(x) if f(x)= In (2x) + cos (6x)

A: Given- f(x)=ln(2x)+cos(6x) To find - f'(x) Here we will use the following formulas-…

Q: The f sin x cos²xdx is x sin 4x {A} 16 64 sin 4x x {B} 16 16 O A B O - sin³2x 48 sin³2x 48 +C + C…

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Q: Suppose f(x) =sin(3x- 2). Evaluate: A -3cos(3x- 2) +C B ® --cos( 3x – 2) +C © ;cos(3x – 2) + C D D…

A: Topic = Integration Correct option = B

Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: Evaluate D6(cosx+e-2*) (A sin x +64e -2 B cos x – 32e-2r (c - sin x – 32e-2x cos x + 64e -2x |

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Q: find for f(x) =|x| . [-x , a] - IT - .a 0.b0 T.cO 2n.dO

A: We have to solve given problem:

Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: Evaluate: Jx?cos(2x)dx A None of the above 2x2sin(2x) – 2xcos(2x) + sin(2x) B + C 2x²sin(2x) +…

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

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Q: Suppose f (x) =cos( 2– 3x). Evaluate: )dx A - 3sin(3x – 2) +C ® -;sin(3x – 2) + C sin(3x – 2) + C D…

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