If k(x )=* +8 * +2 ' -, complete the table and use the results to find lim k(x). X- -2 -2.1 -2.01 -2.001 - 1.999 -1.99 - 1.9 k(x ) Complete the table. -2.1 -2.01 -2.001 - 1.999 -1.99 -1.9 k(x) (Round to three decimal places as needed.) Find the limit. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. x+8 x-+-2 x+2 O B. The limit does not exist and is neither co nor - co. Use the graph to find the following limits and function value for each value of a. ) lim f(x) ii) lim f(x) iii) lim f(x) iv) f(a), if it exists a. For a = 0 b. For a = - 2 a. I) Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. lim f(x) = (Type an integer or a decimal.) x-+0" O B. The limit does not exist. i) Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. lim f(x) = (Type an integer or a decimal.) x-+0' O B. The limit does not exist ill) Select the correct choice below and, if necessary. fill in the answer box within your choice. O A. lim f(x) = (Type an integer or a decimal.) O B. The limit does not exist. iv) Find f(0). Choose the correct answer below. OA. -2 OB. 1 Let lim f(x) =9 and lim g(x) = 3. Use the limit rules to find the following limit. X-+7 X-+7 lim f(x) + g(x) 6g(x) lim f(x)+g(x) X-+7 6g(x) (Type an integer or a simplified fraction.)Suppose that f(x) and g(x) are differentiable functions such that g(5) = 7, g'(5) = 1, f(5) = 2, and f'(5) = 4. Find h'(5) when h(x) = _ g(x) If g'(6) = 4 and h'(6) = 16, find f'(6) for f(x) = =g(x)+ h(x) Which of the following expre ions could be used to compute h'(5)? I'(6) = (Simplify your answer.) O A. f'(5)g(5) - 1(5)g'(5) B. 9(5)f'(5) -f(5)g'(5) [g(5)] O c. f(5)g'(5) - f'(5)g(5) O D. f(5)g'(5) - 9(5)f' (5) Use the graph to find the following limits. [g(5)] (b) lim f(x) h'(5) = (Simplify your answer.) (a) Find lim f(x) or state that it does not exist. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. lim f(x)= Find an equation of the line tangent to the graph of f(x) = (3x - 5)(x + 5) at (2,7). ( Round to the nearest integer as needed.) O B. The limit does not exist. (b) Find lim f(x) or state that it does not exist. Select the correct choice First, find f' (x). below and, If necessary, fill in the answer box within your choice. f' ( x) = O A. lim f(x) = (Round to the nearest integer as needed.) O B. The limit does not exist. For the function below, find the value(s) of x in which f'(x) = 0. 1( x ) = (x2 - 2) (x2 - 15) a) Graph the given function, (b) find all values of x where the function is discontinuous. nd the right at any values of x The values are 3 if x 1 The total cost (in hundreds of dollars) to produce x units of perfume is C(x) = _X- 1. 4x + 3 OA OB O C. (a) Find the average cost fun 15- (b) Find the marginal average c (c) Find the average cost and the marginal average cost for a production level of 20 units. Interpret your results. A psychologist contends that the number of facts of a certain type that are remembered after t hours is given by the following function. 88t 1(1) = ggt - 88 (b) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Find the rate of change at which the number of facts remembered is changing after 1 hour and after 10 hours. O A. The function is discontinuous at x = (Use a comma to separate answers as needed.) Find all points on the graph of f(x) =6x - 15x +9 where the slope of the tangent line is 0. O B. The function is continuous for all values of x. c) Find the limit or limits from the left and from the right for any values of x found in part (b). Select the correct choice below and, if necessary. fill in the answer boxes to complete your choice. The point(s) on the graph of f(x) = 6x - 15x +9 where the slope of the tangent line is O is/are. O A. The limit(s) from the left is/are . The limit(s) from the right is/are Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) (Use a comma to separate answers as needed.) O B. No discontinuities were found in part (b). Find all the values of x where the tangent line to the function f(x) = x - 7x2 - 4x +5 is horizontal. Find the average rate of change of the function over the given interval. y= V3x -2; between x = 1 and x = 2 The solution(s) is/are the value(s) of x that satisfy V =]. That is, solve the equation ]. (Type an equation.) What expression can be used to find the rerage rate of change? 1(2)+ 1(1) Find the point on the graph of the given function at which the slope of the tangent line is the given slope. OB. bra b-1 f(x) = 8x +2x-9; slope of the tangent line = -4 1(2)-1(1) 2 - 1 O D. lim -(2+ h)-1(2) The point at which the slope of the tangent line is - 4 is. (Simplify your answer. Type an ordered pair.) The average rate of change of y between x = 1 and x = 2 is. (Simplify your answer.)