Functions Amplitude Period Phase Shift Vertical Shift 1. y = 2 tan(4x – n) + 3 2. у = 3 cos (x + n) - 2 3. y = 4 sec(2x) 4. y = sin (2x + 6x) + 1 – #) 2n - 4 5. y = 2 csc (x -

Q: Use a computer algebra system to analyze the function over the given interval.…

A: Consider the provided question, Analyzing the given function over the given interval using computer…

Q: ELIMINATION OF ARBITRARY CONSTANTS

A: The given solution curve is y=C1excosx+C2exsinx=ex C1cosx+C2sinx. That means, the roots of auxiliary…

Q: VARIATION OF PARAMETERS 1. (D^2+1)y= sec tanx

A: We have to solve by variation of parameters.

Q: sin x+cosX Differentiate y = %3D sin x-cos x 2 А. 1-sin 2x -2 В. 1+sin 2x -2 С. 1-sin 2x 2 D. 1+sin…

A: Given,  y=(sinx+cosx)/(sinx-cosx)

Q: 12. Find the first derivative of y = 2cos(2 + x?). A. -4x sin (2 + x²) B. 4x cos (2 + x*) C. x sin…

A: Since you have posted multiple questions. As par guidelines we"ll solve first question only. If you…

Q: A tank contains 280 gallons of water and 20 oz of salt. Water containing a salt concentration of (1…

A: Given Information

Q: 4. y = sec-1 Activities in Inverse Trigonometric Functions dy Find the dx 1. y = sin-12x – V1– 4x²…

A:

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

A: First we have to define all transformations.

Q: S 1 dx = (x² + 1)(1 – sec(tan-1 x)) Select one: а. 1 -x + (sin(cos-1x)) b. 1 -tan(cot-1x) +…

A: Hence option (d) is correct .

Q: (3cos³x-1 1- sin?x To evaluate - dx the integrand can be transformed to [(3cos³x + csc?x)dx |Зcosx…

A: Option D is the tranformed integral.

Q: find the critical numbers of the function g(theta) = 4(theta)-tan(theta). My question is from the…

A: Refer to the question as per screenshot provided, I have to answer the how the last step came.That…

Q: Separation of Variable (cos'x-sin x+ sin' xkx + sin x sin y(1- sin x)dy = 0

A: Separation of variables

Q: dy - x = x2 siny dx 3 -2 =-(-siny +cosy + Ce-y/?)*? ANSWER: x = + cosy + Ce

A: We will find out the required solution. Kindly note that there is misprints in question which has…

Q: i.y = sin-1 (x), y € - ii.y = cos-1 (x), y € [0,¤] iii.y = tan-1 (x), y € (- 2'2 (x), y € [-;, 2'2

A: To prove the derivative formula for inverse trigonometry function we keeo the equation in terms of x…

Q: sec 2a cos ydy - (1 sin y) da = 0 %3D

A: Given:     sec(2x) cos2y dy-x(1-siny)dx=0 Re-arranging sec(2x) cos2y dy-x(1-siny)dx=0sec(2x) cos2y…

Q: use radians 2sinx + 1.5e^x + 1.25 Using Newton-Raphson method (upper limit) find the x intercept…

A:

Q: For the function y=-2-sin 2-x-- |+5, determine the properties 2 Amplitude: Period: Phase shift:…

A:

Q: sin(x)cos(2x)sin(3x) dx A B D sin(3x) cos(3x) sin(2x)cos(2x) sin(2x) + + 12 8 sin(3x)cos(3x) 12 +…

A: We have to find integration of given trigonometric term.

Q: a) y = 3 sin 2(x-30°) +1 b) y = 0.25 cos 0.5(x-1)-3 Range Range Amplitude Amplitude Period Period…

A: Part a) Given: y=3sin2x-30°+1

Q: •sin Find the derivative of n x² dx. '2² dæ) = (sin z)° esin 0 '2² dx) = (sin 0)² - cos 0 d_ rsin 0…

A: We have to find

Q: Two spacecraft are following paths in space given by ri = (sin(t), 1, t²) and r2 = (cos(1), 1 -1,r).…

A: Use rate of change of temperature

Q: 9. 2x+4 4 1+ (x + 2)² 1+ (x + 2)² (b) Using suitable method find [2 tan¹(x+2) dx. (a) Find - dx and…

A:

Q: Using Variation of Parameters 4y''-4=cos-1x

A: Given that, 4y''-4=cos-1x Now let's take, 4y''-4=0 Take m=ddx, 4m2-4y=04m2-4=0m=±1 So the homogenous…

Q: sin.x 14. What is y" if y=1-cosx A) y'= B) y'= -COS.X (1 – cosx)? sinx (1-cos.x)² C) y'= D) y'=…

A: Given: y=sinx1-cosx We have to find y''.

Q: cosh (T- i) = %3D e cosl i e sin 1 + e- cos 1 + i e- sin 1 e cosl i e sin 1 + e-TI cos 1 ie- sin 1 2…

A: We know formula of coshx in term of exponential form

Q: f(x)=-cos 6. f(x)=7sin(x) Amplitude:_ Amplitude: Period: Period:

A: Here, the given functions are 1) f(x)=-cosx62) f(x)=7sinx We need to find the "amplitude" and…

Q: dx Half-angle Substitution cos x +sin x-1

A:

Q: A tank contains 120 gallons of water and 45 oz of salt. Water containing a salt (1+-sin t) oz/gal…

A:

Q: Cycloid arch: x = a(0 – sin 0), y = a(1 cos 0) - -

A:

Q: 1. y=(-1/2)In(e^cotx^2) Find: sqrt of (y')x^-1 2. y=arctan(sin e^x) Find: ((y')e^-x)^2 +tanh^2 (e^x)

A: Now we will find y' and then solve the problem.  Here we will differentiate using chain rule.…

Q: 1. Integrate: Transformation by trigonometric formulas X x 1.1 sin sin dx 5

A: Use trigonometric identities,                                          sin2x + cos2x = 1

Q: Displacement of a structure is defined by the next equation for a damped oscillation y = 9ekt cos ot…

A: Given - Displacement of a structure is defined by the next equation for a damped oscillation y =…

Q: tanx - tany = sin(x+y)/cosxcosy

A: The given identity to be proved is,

Q: Function (y) 2 cos(x – 2n) Property -3 cos 6x 3 cos (x +) -2c05지 З cos Period Amplitude Min Value…

A: This question is related to trignometric ratios , We will solve it using given information.

Q: Function (y) cos (x + #) Property -3 cos 6x 5 -2 cos-x 2 cos(x – 2n) Period Amplitude Min Value Max…

A: As for given functions: y=AcosBx-C+D Where  A=Amplitude Period = 2πB Phase shift is C (+ve is to the…

Q: Solve (cos x cos y- cot x) dx-sin x sin y dy = 0 %3D

A:

Q: Maclaurine’s series of ∫((cos^2(x) dx)

A: To find → Maclaurine's series of ∫ cos2 x dxSolution →                       ∫ cos2x dx = ∫ 1+cos…

Q: y. x -. cos(- + cos(- 2 4 х — у, 2 sin(- 4 = cos x - sin y 2

A: Here, the objective is to prove the following: 2sinπ4+x-y2cosπ4+x-y2=cosx-siny

Q: 5. у %3D е2*(с1 cos x + c2 sin x) 5. y = e2*(c1

A:

Q: 2) + (2x tan-" y – x³)(1+ y²) = 0 Ans: tan-y=(x² + 1) + ce-*²

A: Bernoulli differential equation in the form of: dydx+k(x) y=q(x) yn 1yndydx+k(x)×1yn-1=q(x)…

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

A:

Q: O lim メーや 2X-5 /メ -V-オ-2 V x +3 ar conditioning. メーろ 2-x2 ulim メー→/2 | lim 4) "Sina-Cosxsinx; メーO…

A: a.limx→42x-53=2×4-53=1 b. limx→-3=x+4--x-2x+3since numerator is not zero, while only denominator is…

Q: Equation of Axis Function Amplitude Period Phase Domain Range Shift (left or right) y = cos(5x –…

A:

Q: ) Evaluate antan L tc 2 - arctan -x3 - 2 tc arctan 3- 2) Evaluate dx 5 arctan arctan x*-5 +C 45 -…

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Q: cos 2x - cos2a Integrate cos x-cosa

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Q: 1. Using Half Angle Substitution cos x dx Find= S 2-cos x

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

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

Q: The function y = sin X has been transformed. It now has amplitude of 3.4, a period of 36, a phase…

A: This is a question of linear transformation.

Q: A tank contains 220 gallons of water and 45 oz of salt. Water containing a salt concentration of…

A: