Determine the points at which the function f to the right has discontinuities. For each point state the conditions in the continuity checklist below that are violated. 1. f(a) is dened (a is in the domain of f). 2. lim f(x) exists. XPa 3. lim f(x) = f(a) (the value of f equals the limit of f at a). X>a f(x) is discontinuous at x = . (Use a comma to separate answers as needed.) Determine the points in the interval (1 , 6) at which the function has discontinuities. For each point state the conditions in the continuity checklist that are violated. In order for f to be continuous at a, the following three conditions must hold. 1. f(a) is dened (a is in the domain of f). 2. lim f(x) exists. X98 3. lim f(x) = f(a) (the value of f equals the limit of f at a). X98 a f(x) is discontinuous at x = . (Use a comma to separate answers as needed.) Determine the intervals of continuity for the following function. Choose the correct answer below. O A. [0, 2), [2, 3), (3, 6] O B. (0, 2), [2, 3), (3, 6] O C. [0, 1], (1, 2), [2, 3), (3, 6] O D. [0,1),(1,2),[2, 3), (3. 6] 0 1 2 3 4 5 6 7 Determine whether the following function is continuous at a. Use the continuity checklist to justify your answer. 3x2+11x+10 x2 +8x f(x)= ,a=-8 Select all that apply. |:| A. The function is continuous at a = 8. |:| B. The function is not continuous at a = - 8 because f( - 8} is undened. |:| C. The function is not continuous at a = - 8 because Iim f(x) does not exist. x> 8 |:| D. The function is not continuous at a = - 8 because Iim f(x) f( - 8}. x> 8 Determine whether the following function is continuous at a. Use the continuity checklist to justify your answer. 5x - 4 y= a= 4 2 -9x + 20 Select all that apply. A. The function is continuous at a = 4. B. The function is not continuous at a = 4 because f(4) is undefined. C. The function is not continuous at a = 4 because lim f(x) does not exist. X-4 D. The function is not continuous at a = 4 because lim f(x) # f(4). X-+4Suppose f(x) is defined as shown below. a. Use the continuity checklist to show that f is not continuous at 3. b. Is f continuous from the left or right at 3? c. State the interval(s) of continuity. 2 + 3x ifx23 f(x) = 3x if x 3 Choose the correct answer and, if necessary, complete the answer box of your choice. OA- 5x+3I I . . 5x+3I I f 0 II 5x+3 I I 2x4 IS continuous at all pomts at which 2x 4 Is continuous and (a)> .Therefore, x313 2x 4 (Simplify your answer.) 0 B. The limit does not exist. Evaluate the following limit. 2 + sin 0 2 lim 0-0 sin 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A . 2 + sin 0 N lim because sin 0 is continuous for all 0. 0-0 sin 0 (Simplify your answer.) O B. The limit does not exist and is neither co nor - co.Evaluate the following limit. 5( cos x - 1) lim X-0 sin ~ x Change the given indeterminate form into a determinate form. Choose the correct answer below. sin x O A. 5( cot x - 1) 5( cot x - 1) O B. sin x 5 O C. - (1 + cos x) O D. -5(1 + cos x)Determine the interval(s) on which the following function is continuous. Then analyze the given limits. 6 e x f(x) = x ; Iim f(x); Iim f(x) 1 - e x>0 x>0 + O The function is continuous on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) Determine the intervals on which the following function is continuous. Specify right- or left-continuity at the finite endpoints. f(x) = 1x