Find the range, periodicity and phase shift of y = 2 sin (x + 3)

Q: What is the phase shift of the function f(x) = sin(x+ 2)? %3D

A: For any  sinusoidal function f(x) = Asin(Bx + C)  The phase shift is  = -C/B

Q: 3. Evaluate fe cos rdr 4. Evaluate: / tan -1 (3x)dx.

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Q: Determine the phase shift of the function y = sin(x - π/3)

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Q: 11. y = sin 12. y = cos*(-) 13. y = arccos(-) %3D 14. y = arcsin (- 5

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Q: 1 S cos³ 3x sin' 3x dx

A: The given integral is: I=∫cos33xsin43xdx   ...1   We know that; The Power rule: ∫xndx=xn+1n+1+C

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Q: 12. y = −3 cos (0 + 1) − 2 Amplitude: Period: Phase Shift: Midline:

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Q: cos 4x 2 dx sin4x 5.

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Q: 4. y tan (x +) Period Phase Shift Vertical Shift

A: First we have to define all transformations.

Q: 9. Sin 2X dx COS 2X

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Q: 9 sin5(x) cos³(x) dx

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Q: (b) S tan3 x sec² x dx c) S sin³x cos5 x dx

A: The explanation of the solution is :

Q: y = e2* sin 2x + e3* cos 2x

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Q: (2x-ィ) cos 3x dx

A: The given function is, ∫(2x2-1) cos3x dx. Obtain the value of the integral ∫(2x2-1) cos3x dx.…

Q: Where does the periodic function f(x) = 2esin (x/2) take on its extreme values and what are these…

A: Consider the function:  fx=2esinx2 The given function will be maximum when sin(x/2) =1 because the…

Q: cos

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Q: Evaluate the integral

A: Let the given integral be y - y = ∫6sin2x1+cos4xdxy = 6∫sin(2x)1+cos2x2dx…

Q: 6e(6 sin 3x) dx sec 3x

A: Inverse of sec3x is cos3x Cos3x=(1/Sec3x) Putting in the integration problem

Q: c- S cos(Inx).dx

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Q: Cos 2x dx ) Sin*2× + 8 1.

A: Given ∫cos2xsin22x+8dx

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Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral.

Q: Find the first and second derivatives of r = [3 cos 2t, 3 sin 2t , 4t].

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Q: Evaluate cos x -2 sinx sin 2x dx Round to 4 decimal places.

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Q: 2. Find the derivatives of the folowing equations: y = sin-'(1 -t) y = csc-(x/2) y = In(tan- x)

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: 1 dx 6- cos²xsin²x

A: use trigonometric identity to prove the integral

Q: 1. [e-2x sin 2x dx

A: As per the instruction, we will be answering only the first one. For (1),      ∫…

Q: 11. y = 2 sin(0) + 2 Amplitude: Period: Phase Shift: Midline: 2n 3x H 4 ST

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Q: What is the phase shift and vertical shift of f(x

A: Explanation and solutions is given below....

Q: 4 cos () dx 10. x³ sin3

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Q: What is the phase shift of this function? y=sin(3x-15pi)

A: This question is based on Sinusoidal function.

Q: 15. What is the amplitude, period, phase shift and vertical shift of y = sin(40) + 3 A. Amplitude:…

A: Let us first understand the terms. Amplitude is height from center line to peak. Or Distance…

Q: 3x Cos 2x dx

A: Simple use integration by parts method.

Q: 4:    Y = sin-1 2x 5:    Y = sinh-14x

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Q: 3 1. cos x - 5 dx -3

A: The given integral is ∫-34 cosx-3x5dx. Evaluate as follows.

Q: Differentiate the function y = e - 4x  sin   5x

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Q: 3t CoS cos ut}

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Q: 5: - S cos(lnx).dx

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Q: 1. cos 3x dx

A: Since, the exact question was not specified so will answer very first question of it. Please…

Q: 1.y= 3 sin (x -) – 1 Amplitude Period Phase Shift Vertical Shift

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Q: f(x)%3Dcos =cOS X- Amplitude %3D Equation of mid-line: Length of period: Phase Shift:

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Q: 1) f (x) = 4sin3 (x +-) – Amplitude: Midline: Period: Phase Shift:

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Q: e phase shift of y = -3 + 3 sin

A: The given equation is y=-3+3sin6x-π2.

Q: 1) y= sinx + 2 Vertical Shift: Phase Shift:

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Q: evaluate the integral.

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Q: [cos 3x cos 4x dx

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Q: За (cos 4x sin 3x – sin3 x)dx a

A: Given: I=∫a3asin3xcos4x-sin3xdx We know that sinAcosB=sinA+B+sinA-B2…

Q: Differentiate  cos(t^2 - 6)

A: Given: cost2-6

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A: Given query is to find the derivative of cos-1(-3x).

Q: 6sin³ (2x) cos(2x) dx =

A: the given indefinite integral is: ∫6sin52xcos2xdx we have to find the value of the given indefinite…