4. The period of a pendulum is given by T = 3 1 , where L is the length of the pendulum in feet, 3 = 32 ftfsec2 7r 8' which is the force of acceleration due to gravity, and Tis the period of the pendulum given in seconds. If the length of a pendulum is measured to be 3 feet long and it is known that the maximum error in the measurement is within one-eighth of an inch, then what is the approximate maximum error in calculating the pendulum's corresponding period? Use differentials to approximate. 5. Given below is a table of values sampled om a survey of men the age of 30 which measures M, the percent of body muscle increase of the men who took a certain muscle building supplement for 4 weeks while also exercising for at least 30 minutes per day, based on their weight w, in pounds. M (a) Using the symmetric difference quotient, nd an estimate for the value of M '(220). (b) Use your result from part (a) to approximate the value of M (222) . Section 4.5 Activity Linear Approximations and Differentials 1. Ifwe know that f(x) is differentiable and exists near x = a, and that f'(a) = 7: with f(a) = 6 , then nd the formula for L(x) , the linear approximation of f (x) at x = a. 2. Let f(x) = {I}. (a) Find the linear approximation of f (x) atx = 8. (b) Use your result from part (a) to approximate 318.8 . (c) What is the error (good to 8 decimal places) in your approximation in part (b) compared to the actual value of {la8? 3. Assume that L(x) is the linear approximation of a differentiable function f(x) at x = a, with f "(0)