2.7 Homework - Derivatives, Rates of Change (Homework)

6. [-/1 Points] DETAILS SCALCET8 2.7.041. MY NOTES ASK YOUR TEACHER The limit represents the derivative of some function f at some number a. State such an fand a. lim cos(It + h) + 1 h - 0 h Of ( x) = cos(x), a = 0 O f( x) = cos(x), a = n Of(x) = cos(x), a = 1/3 Of ( x) = cos(x), a = 1/4 Of( x) = cos(x), a = 1/6 Need Help? Watch It 7. [-/1 Points] DETAILS SCALCET8 2.7.046. MY NOTES ASK YOUR TEACHER A roast turkey is taken from an oven when its temperature has reached 185F and is placed on a table in a room where the temperature is 750F. The graph shows how the temperature of the turkey decreases and eventually approaches room temperature. By measuring the slope of the tangent, estimate the rate of change of the temperature after an hour. OF/min T (F) 200 P 100 0 30 60 90 120 150 t (min)8. [-/1 Points] DETAILS SCALCET8 2.7.057. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The quantity of oxygen that can dissolve in water depends on the temperature of the water. (So thermal pollution influences the oxygen content of water. ) The graph shows how oxygen solubility S varies as a function of the water temperature T. (mg/L) 16- 12- 8 4- 8 16 24 32 40 T(C) (a) What is the meaning of the derivative S '(T)? O S '(T) is the rate at which temperature changes with respect to the oxygen solubility. O s '(T) is the rate at which temperature changes with respect to the temperature. O s '(T) is the rate at which oxygen solubility changes with respect to the water temperature. O s '(T) is the rate at which oxygen solubility changes with respect to the oxygen solubility. O s '(T) is the current level of oxygen solubility for a given temperature. (b) Estimate the value of S '(16). (Round your answer to three decimal places.) S '(16) (mg/L)/C Need Help? Watch It9. [-/1 Points] DETAILS SCALCET8 2.7.059. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Determine whether f '(0) exists. A( x ) = 1 x sin (3) if x # 0 if x = 0 Of '(0) does exist. Of '(0) does not exist.10. [-/1 Points] DETAILS SCALCET8 2.7.JIT.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. y = (x - 3)2 +5 5 X X -10 -5 5 10 -10 -5 10 -5 -5 -10 O -10 O y 101 10- 5 - X LX -10 -5 5 10 -10 -5 5 10 -5 -5 -10 -10 O O