X-+2 X-+2 Let lim f(x) = 2 and lim g(x) = 8. Use the limit rules to find the following limit. (a) Graph the given function, (b) find all values of x wt had the right at any values of x where the function is discontinuous. m f(x)+g(x) 11 1x 3 5.9 5.99 5.999 6.001 6.01 6.1 lim (x)+9(x)= x-+2 2g(x) (a) Choose the correct graph of the function. (Type an integer or a simplified fraction.) OA. OB O c. CID 15 Q Complete the table. x 5.9 5.99 5.999 6.001 6.01 k(x) 0 (Round to three decimal places as needed.) (b) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Find the limit. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The function is discontinuous at x = Use the graph to find the following limits and function value (Use a comma to separate answers as needed.) O A. for each value of a. O B. The function is continuous for all values of x. X -216 () lim f(x) ") lim f(x) ill) lim f(x) iv) f(a). if it exists. x x-+6 x-6 x-+a" x-a' (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. O B. The limit does not exist and is neither co nor - co. a. For a = 0 b. For a = 2 O A. The limit(s) from the left is/are . The limit(s) from the right is/are (Use a comma to separate answers as needed.) O B. No discontinuities were found in part (b). 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.) Use the graph to find the following limits. For the function below, find the value(s) of x in which f'(x) = 0. *-+0" O B. The limit does not exist. (a) lim f(x) (b) lim f(x) 1(x ) = (x2-3) (x2 -13) ") Select the correct choice below and, if ne sary, fill in the answer box within your choice. O A. lim f(x) = (Type an integer or a decimal.) (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 B. The limit does not exist. The values are]. O A. lim f(x) = i) Select the correct choice below and, if necessary, fill in the answer box within your choice. (Use a comma to separate answers as needed. Round to three decimal places as needed.) (Round to the nearest integer as needed.) O A. lim f(x) = (Type an integer or a decimal.) O B. The limit does not exist. (b) Find lim f(x) or state that it does not exist. Select the correct choice O B. The limit does not exist. below and, if necessary, fill in the answer box within your choice. iv) Find f(0). Choose the correct answer below. O A. lim f(x) = Find all points on the graph of f(x) = 16x2 - 36x + 14 where the slope of the tangent line is 0. OAO (Round to the nearest integer as needed.) O B. 1 O B. The limit does not exist. ( C. The answer is undefined. OD. -2 The point(s) on the graph of f(x) = 16x" - 36x + 14 where the slope of the tangent line is O is/are]. b. i) Select the correct choice below and, if ne swer box within your choice. (Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) O A. lim f(x) = (Type an integer or a decimal.) Find the average rate of change of the function over the given interval. x-+2" y= 12x + 3; between x = 3 and x = 11 O B. The limit does not exist. i) Select the correct choice below and, if necessary, fill in the answer box within your choice. What expression can be used to find the average rate of change? O A. lim f(x) = (Type an integer or a decimal.) Find the point on the graph of the given function at which the slope of the tangent line is the given slope. x-+2* O A. (11)+ f(3) O B. The limit does not exist. f(x) = 8x2+4x -6; slope of the tangent line = - 3 ii) Select the correct choice below and, if necessary, fill in the answer box within your choice. O B. lim (6)-f(3) bra b-3 O A. lim f(x) = (Type an integer or a decimal.) O C. lim (11 + h)-f(11) h X-+2 O B. The limit does not exist OD. (11)-1(3) The point at which the slope of the tangent line is -3 is]. 11- 3 (Simplify your answer. Type an ordered pair.) iv) Select the correct choice below and, if necessary, fill in the answer box within your choice. The average rate of change of y between x = 3 and x = 11 is]. (Simplify your answer.) O A. f(2) = (Type an integer or a decimal.) O B. The answer is undefined.1. Use the properties of limits to evaluate the following limits, if the limit exists. . x22x15 a. 11m x>3 x+3 d lim 9x3+7x4 ' xam2x48x2+5 2. Using your graphing calculator and your knowledge of functions and algebra, find all values x = a where the function is discontinuous. For each such x value, evaluate the limit as x approaches a. a. W) = Ix7I x+2 x2+2x b. f(x) = 3. Use the limit definition of the derivative to calculate f'(x) for each function. a. f(x) = 4x2 6x 8 b. f(x) = x 4. Using the result from problem 3b, calculate the equation of the tangent line to the curve at x = 4. 5. The cost to fly x miles on American Airlines could be approximated by the equation 60;) = 0.000003964x+ 191.16. The average cost per mile, denoted by 5(x), is found by dividing C(x) by x. Find and interpret lim 5(96). xbCCI Source: Expedia