Consider the single variable function defined by y = 4x - x. a. Find a parameterization...

 

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Consider the single variable function defined by y = 4x² - x³. a. Find a parameterization of the form r(t) = (x(t), y(t)) that traces the curve y = 4x² 4x²x³ on the interval from x = -3 to x = 3. - b. Write a definite integral which, if evaluated, gives the exact length of the given curve from x = -3 to x = 3. Why is the integral difficult to evaluate exactly? c. Determine the curvature, k(t), of the parameterized curve. might be useful here.) d. Use appropriate technology to approximate the absolute maximum and minimum of (t) on the parameter interval for your parameterization. Compare your results with the graph of y = 4x² - x³. How do the absolute maximum and absolute minimum of (t) align with the original curve? Consider the single variable function defined by y = 4x² - x³. a. Find a parameterization of the form r(t) = (x(t), y(t)) that traces the curve y = 4x² 4x²x³ on the interval from x = -3 to x = 3. - b. Write a definite integral which, if evaluated, gives the exact length of the given curve from x = -3 to x = 3. Why is the integral difficult to evaluate exactly? c. Determine the curvature, k(t), of the parameterized curve. might be useful here.) d. Use appropriate technology to approximate the absolute maximum and minimum of (t) on the parameter interval for your parameterization. Compare your results with the graph of y = 4x² - x³. How do the absolute maximum and absolute minimum of (t) align with the original curve?

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Lets address each part of the problem a To parameterize the curve y 4x x we can set xt t and yt 4t2 ... View the full answer