two friends are trying to figure out how many supernova explosions there will be by looking at the function given by NASA. f(x)= Sin (2x) -1-cos(2x) where x represents the days that it will happen.

Q: 7x+2 If h(x) = ln| find h' (x). 3 x 2 sin x

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Q: Find the general solution of f′(x) = −2x sin x2 .

A:

Q: h(x)=3sinh(1–3x² )cosh(1–3x² )

A: Sinh^-1(x)= ln(x+[√x^2+1]) Cosh^-1(x)=ln(x+[√x^2-1])

Q: if f(x)=ln(1+cosx) then find f`(x)

A: f'(x)=(1+cos(x))'/(1+cos(x))      =-sin(x)/(1+cos(x))

Q: 4. y = 2Cos(x)Sin(2x) – Sin(x)Cos(2x) %3D

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Q: (cos 2x) f (x) = e

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Q: If f(x) = sinh³ x %3D the en f'(x) = ||

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Q: A periodic function is defined in one period as |-sin(폭),-2sx<-1; f(x)={ 1 [x+1, -18x50.

A: In this question, we draw the function in a given domain and find the Fourier series of the…

Q: Evaluate: [ cos 2x log(1+ tan x) dx

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Q: Consider the function f(x) whose second derivative is ƒ''(x) = 9x + 6 sin(x). If ƒ(0) = 4 and f'(0)…

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Q: sin (x+1) dg(x) de f(x) +Vx+5 2 given f(x)= 3x + In 5x and g(x)=: Find

A: This is very complicated &amp; lengthy problem.We have to think deeply to solve this…

Q: Find f' (x), if f(x) = sin(2x* – sin(x))

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Q: 1. Determine the range of the function y = -3 sin[4(x – 2)] + 2.

A: Range of trigonometric function

Q: If f(x) = (52² + lx + 6)cos(x), find f'(x) =

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Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: Find F(x), f"(x) and f''(x) for f(x)=13x2+ sin(15x).

A: Given,            fx=13x2+sin15x

Q: Find ∫e^(2x)sin(2x)dx

A: Given: ∫e2xsin(2x)dx

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Use the basic definition of Cosh to find the derivative of the function, Coshx=ex+e-x2. Find the…

Q: In this problem, please evaluate the trig functions without a calculator and de tion of the tangent…

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Q: If f(x) = 7 sin(8a)sin-(x), f'(x) -

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Q: sinh 3x –1 H(x)=: 1+cosh 3x –1

A: Given: H(x)=sinh3x-11+cosh3x-1 To solve: The given function.

Q: 2- Solve the equation for x : Cosh x = Sinh x +1/2.

A: We need to find out the value of x. The given equation is Cosh x=Sinh x+12 Now,  Cosh x=ex+e-x2  and…

Q: sin (x+1) 5. Find dx g(x), given f (x) = 3x +In |- 5x and g(x)=: +Vx+5

A: Use derivative rules

Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: 1. f(x) = cos (-:-)

A: From graph, it is clearlimx→∞cos1x =limx→-∞cos1x = 1

Q: 4. Determine the equation of the axis of the function f (x) = -3 sin (x – 2)- 6

A: Given that: f(x)=-3sinπ4(x-2)-6

Q: Solve for x in the interval 0 < x < 2n. log (sin (x)) – log (cos (x)) = 0 a) x = 5,

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Q: Evaluate : sec'x log (1+ sin°x) dx X,

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Q: If f (x) = sin³ (2x) +x², find f" (*). 3 TC 4

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Q: Q3: Find value of x if 3 cosh x- sinh x= 4

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Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

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Q: A water ride with heights above and below the starting point can be modeled by the function y = 3…

A: Given that the height of the Water ride above the function is modelled byy=3sin(π2(x+3)-2).WE neeed…

Q: Is f (x) = x sinx a periodic function ?

A: Introduction :

Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: Find f'(x) if f(x) = e3X sin 2x

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Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: Evaluate 不12 Sin^ x dx = 「ズ「() 2 2r/2+2 n > -1 (Gamma function).

A:

Q: Does x2 - 10 = x sinx have a real solution? Show your process. -

A: Let f(x)=x2-10-xsinx  Then it is clear that f is a continuous function on R. Now…

Q: If f (x) = e2*[sin(x)]², what is f' (x)?

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Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on . (³347) 3π 5π 2' 2

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Q: h(x) = sin 2x cos 2x

A: Product Rule of differentiation: If fx  and  gx are any two differentiable functions, then…

Q: Find 1-x if y = cos-l dx 1+x²

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Q: Find the critical numbers of the function g(x)=8x+sin8x

A: Given data: The expression for the given function is g(x)=8x+sin8x. The differentiation of the given…

Q: If f(x) = cos(ln(x5)), find f ′(1).

A: Given that          f(x) = cos(ln(x5)) Here we have to find f'(1).

Q: 1. Use the following methods to solve for the root of the equation f(x) = xe * – sinx

A: Let f(x)=xe-x-sin2x Given initial approximation is x1=0.5 then…

Q: 3 1 Find: S 2x3 --+ sin(x) dx x2

A: Consider the integral

Q: If g (x) = sinx dx and g =3, then g (0) is equal to

A: