Let f (x) = sin(ax + b) and let g (x) = cos(ax + b) where a and b are constants. Gues a formular for f“(x) and g*(x) for general n (positive integer )

Q: If f(x)=2 sin x/1+cos x, then f′(x) =    f′(4) =

A: We have to find

Q: If f(x)= cos (x)+3x , what is f'(x) ? COS O f'(x)=-sin (x) +3

A: First option is correct. Explanation is given below....

Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

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Q: Find all values of x in the interval [0, 2π] that satisfy (cos x)2 − 3 sin x − 3 = 0

A: x=3π2 is the only values that satisfy the given condition see the calculation below

Q: (b) Let f(x) = sin (cos-1 (sin(cos-vx))).B f'(1) = using chain rule, show that %3D

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Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: If f (x) = – sin(x), then f (10) (x) is equal to A - sin(x) В - cos(x) C sin(x) D cos(x)

A:

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

A: Given

Q: Determine ƒ such that (1, sin 1) is on the graph of f and e2z + 5e² + sin æ ifx 0

A: When derivative function is given, to find the actual function integrate the given derivative of the…

Q: 2. Find the domain of the function. cos x b. f(x) = 1 - sin x

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Q: Find constants c1 and c2 such that: F(x) = c1 sin(3x) + c2x cos(3x) is an antiderivative of f(x) =…

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Q: Find f(x) given that: f'(x) = 2 cos x -3 sin x and f (주) %3D %3D

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Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

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Q: x2 – 1 - if x <1 x – 1 - f(x) = T In x a cos 2rx + b sin(- 4 In 2 if 1<x < 4 if 4 < x where a and b…

A: Explanation of the answer is as follows

Q: Given f (x) = |x| for x E [–n, 1] Show that 4 cos(2n – 1)x |x| = 2 E - - - (2п — 1)2 n=1

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Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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Q: 2 V9 - f(x) = for -3 <x <0 TTX -x +3 coS for 0 < x < 4

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Q: Give an example of a (discontinuous) function that does not satisfy the conclusion of the IVT on…

A: Given: f(x)=sin1x    x≠00            x=0

Q: If f(x) = x² + cos(x), what is f" (x)?

A:

Q: Show that (Aetkx + Be-ikx)and (C cos kx + D sin kx) are equivalent ways of writing the same function…

A: eix  = cos(x) + i sin(x) e-ix = cos(x) - i sin(x)

Q: Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f (x) = x − cos x has a…

A: Consider  Where x belongs to the interval [0, 1] Since x and cos x both are continuous on [0, 1].…

Q: Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that          f(x) = x - cosx…

A: As the intermediate value theorem states that if a function is continuous on a closed interval [a,b]…

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: - cos(x) - 1, choose all values of c in the interval (, 5 For f(x) guaranteed to exist by Rolle's…

A: For fx=-cosx-1, choose all the values of c in the interval π2,5π2guaranteed to exist by Rolls's…

Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x + 2 = 0. b. Express tanh x in terms of e*…

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Q: If f(x) = 3 cos(5 In(x)), find f'(x). Find f'(1).

A: topic - derivatives

Q: Determine f such that (1, sin 1) is on the graph of f and e2z + 5e² + sin x ifæ 0

A: Given f'x=e2x+5ex6ex+sinx    if x&lt;01                           if x=0x5x2+1+cosx if x&gt;0 We…

Q: Find the points of discontinuity of cos () for |x| 1 Determine the type of discontinuity and…

A: Given: gx=cosπx2, for x&lt;1x-1, for x≥1 To Determine: Type of discontinuity and whether g is left…

Q: Find all values of x in the interval [0, 2π] that satisfy the equation.   2 cos x - 1 = 0

A: From the given problem: 2cosx-1=0 Now solve: 2cosx-1=02cosx=1cosx=12cosx=cosπ3

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: (5) Use the Intermediate Value Theorem to prove that xe* = cos(x) has a solution.

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Q: If f(x) = 5 sin x + 2 cos x, then f'(x) :

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Q: Let f be a function defined by f (x) = - x sin (x) + x°. Also consider that for the function g…

A: This is question related to expansion and power series

Q: 7. Determine f (x) so that | cos(In°x) f (x) dx = sin(In²x) + C 2 In x In x (а) 2 In x (c) - (d)?

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Q: If f (x) = - sin(x), then f (11) (x) is equal to A - sin(x) B - cos(x) sin(x) D cos(x)

A: Differentiate 11 times

Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: Prove the identity. cosh(x) + sinh(x) - e

A: To prove the given identity we uses basic expression for sinh(x) and cosh(x).

Q: If f(x) = 3 cos(3 In(x)), find f'(x).

A: Consider the function  f(x)=3cos3ln(x)

Q: 4. Find the absolute maximum and minimum values of the function f(x) = cos²x-3 sinx on the interval…

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Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x +2 = 0. b. Express tanh x in terms of e*…

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Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: Show that y = sin x, y = cos x, and y = a cos x + b sin x (aand b constants) all satisfy the…

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Q: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

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Q: Express T(x)sin x-root(3)cos x into the form of T(x)=Asin(x+theta) , where A>0

A: Sin(A+B)=sinAcosB + cosAsinB

Q: Determine if g is differentiable at a = 0 if 2 cos-1 if – 1 0. x + cos x

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Q: Given f (x) = |x| for x € [-,1 Show that cos(2n – 1)x (2n – 1)2 4 |x\ = ; 2 n=1

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Q: Given f(x) = 3 sin x cos x, find f prime (x)

A: Derivative problem.....

Q: Find the function f(x) if f'(x) = 2 cos x + 3 sin x and f(0) = 4

A: We have

Q: If g(x) f'(x) and if g(x) (cos x - x sin x)e*cosx, then f g(x) tan(f(x))dx is x cosx In(e*cosx) +€…

A: