Q: Given the functions f(x)= x^2 -2x+1 and g(x) =5x-4 determine: (a) g(4) -g(3). (b) f{g(2)}
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Q: Σ k=1 3k! k Choose the correct answer below. A. The series converges absolutely. B. The series…
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A: Given: f''(x) = 4 f'(2) = 11 f(2) = 16
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Q: Find y as a function of t if y(0) = 7, 3/(0) = 6. y(t) = 49y" + 140y + 136y = 0,
A: The given DE is: 49y''+140y'+136y=0 So, the auxiliary equation of it is:…
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A: Solution is given below:
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Q: . Sketch the graph of g(x)=sin7x, using the amplitude and th period.
A: To sketch the graph of the function
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A: Given :Function :y=1y=cos2x
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Q: (b) x-2º dr
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Q: 1.3 domain: What is the domain of y = ln (x² - x - 6)? help (inequalities)
A: The function is y=ln(x2-x-6)
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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…
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Q: Find the total differential. z = 10x4y5 dz = (No Response)
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Q: Σ k=1 (k!)² 5(2k)! Select the correct choice below and fill in the answer box to complete your c…
A: We need to find out that the given series converges or diverges by using the ratio test.
Q: (c) sin(3x) sin(x)dx
A: Evaluate : ∫sin(3x)sin(x) dx
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A: To find out fxgx
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A: The solution is given below
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Q: 5. Evaluate π/3 π/6 cos3 x sin−2 xdx.
A: 5.Solution…
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A: Using ÷ cscx=1sinx 1sin2x-8=0 1sin2x=8 sin2x=18 Now taking inverse and finding values of x we get…
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A: A detailed solution is given below
Q: 4. Set up an iterated double integral equal to the volume of the solid in the first octant bounded…
A: Solution is given below:
Q: 1 10. Sketch the graph of g(x)= - - cos7x, using the amplitude and the period. 7
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Q: | 6. Use a trigonometric substitution to evaluate x³√x²-4 dx.
A: We will find integral using trigonometric substitution.
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A: topic - functions
Q: x=-2 of f(x)=√x²-1
A: Above question is solved.
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Q: 9. Prove: csc(x)-csc(x)cos² (x) = sin(x)
A: To prove: csc(x)-csc(x)cos2(x)=sin(x) Note that, sin2(x)+cos2(x)=1
Q: 1. What is the average rate of change of the function f(x) = x² - 4x + 7 on the interval 1 ≤ x ≤ 3?
A: average rate fo change in an interval (a,b) =f(b)-f(a)b-a
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Q: Find the general solution of the differential equation y(4) - 4y" = t² + et.
A: Given :y4-4y''=t2+et
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A: Given y = x3-24 lnx+7, 12, 3.
Q: 1. Use the substitution method to evaluate S₁² VAZ ²³ + 50 dx
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Q: 5. From the top of a building a bicycle is seen. The distance between the bicycle and the base of…
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Q: We are trying to prove a certain limit. One of the steps in the proof is to show that for every &> 0…
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Q: -5 M -3 -2 5 4 3 -1 3 -5 3 4 a The function graphed above is: Increasing on the interval(s) Submit…
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Q: 2. Find the area bounded by y = x² - 2 and y = 2x + 1.
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Q: Fill in each blank with an angle between 0° and 360° such that sin 220° = sin and cos 220° = cos 0
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Q: A plane begins its takeoff at 2:00 p.m. on a 2170-mile flight. After 5.1 hours, the plane arrives at…
A: We need to fill in the blanks.
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- Graphical Reasoning Use the formulas for the area of a circular sector and arc length given in Section 1.1. (a) For =0.8, write the area and arc length as functions of r. What is the domain of each function? Use a graphing utility to graph the functions. Use the graphs to determine which function changes more rapidly as r increases. Explain. (b) For r=10 centimeters, write the area and arc length as functions of . What is the domain of each function? Use the graphing utility to graph the functions.Sales The table shows the average sales S (in millions of dollars) of an outerwear manufacturer for each month t, where t=1 corresponds to January. (a) Create a scatter plot of the data. (b) Find a trigonometric model that fits the data. Graph the model with your scatter plot. How well does the model fit the data? (c) What is the period of the model? Do you think it is reasonable given the context? Explain. (d) Interpret the meaning of the model’s amplitude in the context of the problem.Vibrating String When a violin string vibrates, the sound produced results from a combination of standing waves that have evenly placed nodes. The figure (1) illustrates some of the possible standing waves. Lets assume that the string has length . a.For fixed t, the string has the shape of a sine curve y=Asinx. Find the appropriate value of for each of the illustrated standing waves. b.Do you notice a pattern in the values of that you found in part a? What would the next two values of be? Sketch rough graphs of the standing waves associated with these new values of . c.Suppose that for fixed t, each point on the string that is not a node vibrates with frequency 440Hz. Find the value of for which an equation of the form y=Acost would model this motion. d.Combine your answers for parts a and c to find functions of the form y(x,t)=Asinxcost that model each of the standing waves in the figure. Assume that A=1. Figure (1)
- Astronomy The table shows the percent y (in decimal form) of the moon’s face illuminated on day x in the year 2018, where x=1 corresponds to January 1. (a) Create a scatter plot of the data. (b) Find a trigonometric model for the data. (c) Add the graph of your model in part (b) to the scatter plot. How well does the model fit the data? (d) What is the period of the model? (e) Estimate the percent of the moon’s face illuminated on March 12,2018.HOW DO YOU SEE IT? Use the figure below. (a) Are all of the trigonometric functions of t defined? Explain. (b) For those trigonometric functions that are defined, determine whether the sign of the trigonometric function is positive or negative. Explain.Angle of Elevation The height of an outdoor basketball backboard is 1212 feet, and the backboard casts a shadow 17 feet long. (a) Draw a right triangle that gives a visual representation of the problem. Label the known and unknown quantities. (b) Use a trigonometric function to write an equation involving the unknown angle of elevation. (c) Find the angle of elevation.
- Modeling Ocean Tides In one day, there are two high tides and two low tides in equally spaced intervals. The high tide is observed to be 6 feet above the average sea level. After 6 hours pass, the low tide occurs at 6 feet below the average sea level. In this task, you will model this occurrence using a trigonometric function by using x as a measurement of time. Assume the first high tide occurs at x = 0. Part E What is the height of the tide after 93 hours? 15pxSolve using derivatives of trigonometric functions. Provide illustrations. A gutter having trapezoidal cross-section is to be made by bending a strip of tin 1 meter wide. If the width of base is 50cm, what width across the top gives the greatest carrying capacity?[Classical Geometries] How do you solve this question? Use the definition of tan alpha in the picture given
- Explain how the graph of r(x)=-3tan(1/2x) is related to the graph of the basic trigonometric function f(x)=tanx Part I: What kind of reflection does the basic function experience? Part II: What is the vertical stretch factor of the function R(x)? Vertical shift ; none Part III: What is the horizontal stretch factor of the function R(x)?Find the relative extrema of the trigonometric function in the interval (0, 2pi). Use a graphing utility to confirm your results. See Examples 6 and 7. (If an answer does not exist, enter DNE.) y = 1/3sec(x) Relative Maximum (x,y)= Relative Minimum (x,y)=Modeling Ocean Tides In one day, there are two high tides and two low tides in equally spaced intervals. The high tide is observed to be 6 feet above the average sea level. After 6 hours pass, the low tide occurs at 6 feet below the average sea level. In this task, you will model this occurrence using a trigonometric function by using x as a measurement of time. Assume the first high tide occurs at x = 0. Part A What are the independent and dependent variables? Part B Determine these key features of the function that models the tide: amplitude period frequency midline vertical shift phase shift Part C Create a trigonometric function that models the ocean tide for a period of 12 hours. Part E What is the height of the tide after 93 hours?