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\f11. [11 Points] OSEALC1 4.1.044' CDnsider the baseball diamond, which has sides of 90 ft. A batter hits the ball and runs [award rst base at e speed of 24 me. At what rate (in fl/s) does the distance between the runner and secnnd base change when the runner has run an 91? (Round your answerlu twn decimal planes.) |:st 1. [-/1 Points] DETAILS OSCALC1 4.2.051. Find the linear approximation L(x) to y = f(x) near x = a for the function. A ( x ) = _ , a = 6 L ( X ) = 1 2. [-/1 Points] DETAILS OSCALC1 4.2.055. Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = sin (x), a = 0 L ( x ) = 3. [-/1 Points] DETAILS OSCALC1 4.2.058. Compute the value given within 0.01 by deciding on the appropriate f(x) and a, and by evaluating L(x) = f(a) + f'(a)(x - a). Check your answer using a calculator. cos(0.01) 4. [-/2 Points] DETAILS OSCALC1 4.2.062. Determine the appropriate f(x) and a, and evaluate L(x) = f(a) + f'(a)(x - a). (0.98) Calculate the numerical error in the linear approximation. (Round your answer to five decimal places.)5. [-/2 Points] DETAILS OSCALC1 4.2.066. Determine the appropriate f(x) and a, and evaluate L(x) = f(a) + f'(a)(x - a). (1 + 1 )10 Calculate the numerical error in the linear approximation. (Round your answer to five decimal places.) 6. [-/2 Points] DETAILS OSCALC1 4.2.072. Find the differential. = 6X4 - x+ 9 dy = Evaluate for the given x and dx. x = 2, dx = 0.1 dy = 7. [-/2 Points ] DETAILS OSCALC1 4.2.077. Find the differential. y = x' + 2x + _, x = 1, dx = 0.05 dy = Evaluate for the given x and dx. X = 1, dx = 0.05 dy = 8. [-/1 Points] DETAILS OSCALC1 4.2.078. Find the change in volume dV (in units) if the sides of a cube change from 11 to 11.1. dv = units