Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. _ 5+x _x(x8) f(x) Choose the correct answer below. There is a discontinuity at x = 0. The limit does not exist. There is a discontinuity at x = 0, x = 8, and x = 5. For all three points, the limit does not exist. There is a discontinuity at x = 8. The limit does not exist. There is a discontinuity at x = 0 and at x = 8. For both points, the limit is 5. V There is a discontinuity at x = 0 and at x = 8. For both points, the limit does not exist. The body mass of a certain type of sheep can be estimated by M(t) = 25.5 + 0.4t 0.001t2 where M(t) is measured in kilograms and t is days since May 25. 3. Find the average rate of change of the mass of a sheep between 105 and 115 days past May 25. b. Find the instantaneous rate of change of the mass of a sheep whose age is 105 days past May 25. c. Graph the function M(t) on [5, 125] by [25, 65]. d. Does the behavior of the function past 125 days accurately model the mass of the sheep? Why or why not? {I) a. Which of the following is the correct expression for the average rate of change between days 105 and 115? M(115)M(105) x W115) W105) 105 115 105 M(115)M(105) w M(115)M(105) 115 115 105 The average rate of Change of the mass of the sheep between days 105 and 115 is 0.180' kg per day. (Type an integer or a decimal.) b. Which of the following is a correct expression for the instantaneous rate of change on day 105? M('lO5+h)-M(105) M(105+h)- M(105-h) \"k Iim X Iim h>O h h>O 105 M(105+h)M(105) M(105+h) M(h) Iim Iim h>O 105 h>O h The instantaneous rate of change of the mass of the sheep whose age is exactly 105 days past May 25 is 0.190' kg per day. (Type an integer or a decimal.) c. Graph the function on [5, 125] by [25, 65]. Choose the correct graph below. d. Does the behavior of the function past 125 days accurately model the mass of the sheep? Why or why not? * No, because after 125 days the mass of the sheep will begin to decrease and eventually go down to O. x Yes, because after 125 days the mass of the sheep will begin to decrease and eventually go down to 0. Yes, because after 125 days the graph will continue to increase forever which represents the given function. Find the average rate of change for the function over the given interval. 7 V= between x = - 4 and x = 0 X - 7 I.. The average rate of change is 11 (Simplify your answer. )Find the value of the constant k that makes the function continuous. 2x -- 3x - 9 if x # 3 g (x) = x - 3 kx - 3 if x = 3 k = 4Using the definition of the derivative, nd f'(x). Then find f'( 3), f'(0), and f'(4) when the derivative exists. f(x)=2x3 +10 (E Find f'(x) using the definition of the derivative. f'(x) = 6x2 Find f'( 3) if the derivative exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. v f'( 3) = 54 (Simplify your answer.) The derivative does not exist. Find f'(0) if the derivative exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. v f'(0) = O (Simplify your answer.) The derivative does not exist. Find f'(4) if the derivative exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. v f'(4)= 96 (Simplify youranswer.) The derivative does not exist