Determine the following limit, using 00 or - 00 when appropriate, or state that it does not exist. lim csc 9 9)-1c Select the correct choice below, and ll in the answer box if necessary. A. The limit does not exist and is neither co nor - co. lim csc 8 = Find all vertical asymptotes, x = a, of the following function. For each value of a, evaluate lim f(x), lim f(x), and lim f(x). Use co or - co when appropriate. x-at x-a x-a x3 - 9x2 + 20x f( x ) = x2 - 5x . . . Find all vertical asymptotes. Then evaluate lim f(x), lim f(x), and lim f(x). Select the correct choice below, and fill in the answer box if necessary. x-at x-a X-a O A. The vertical asymptote is x = . The limits at this vertical asymptote are lim f(x) = lim f(x) = and lim f(x) = x-at x-a x- a O B. The vertical asymptote is x = . The limits at this vertical asymptote are lim f(x) = lim f(x) = and lim f(x) does not exist and is neither co nor - co. x-at x-a x- a O C. There is no vertical asymptote.Determine the points in the interval (1, 6) at which the function has discontinuities. For each point state the conditions f(x) is discontinuous at x =. in the continuity checklist that are violated. In order for f to be continuous at a, the following three conditions must hold. (Use a comma to separate answers as needed.) 1. f(a) is defined (a is in the domain of f). 2. lim f(x) exists. Select the correct choice below and, if necessary, fill in the answer box within your choice. x-a 3. lim f(x) = f(a) (the value of f equals the limit of f at a). x-a O A. The point(s) at x = violate(s) the first condition in the continuity checklist. (Use a comma to separate answers as needed. 61 O B. No points violate the first condition in the continuity checklist. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The point(s) at x = violate(s) the second condition in the continuity checklist. 2- (Use a comma to separate answers as needed.) O B. No points violate the second condition in the continuity checklist. Note that the third condition is automatically violated if either the first or the second condition is violated. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The point(s) at x = violate(s) the third condition in the continuity checklist. (Use a comma to separate answers as needed.) O B. No points violate the third condition in the continuity checklist.Suppose f(x) is defined as shown below. a. Use the continuity checklist to show that f is not continuous at 0. b. Is f continuous from the left or right at 0? c. State the interval(s) of continuity. x + 2x +4 ifxso f ( x) = 4x3 if x > 0 a. Why is f not continuous at 0? O A. lim f(x) does not exist. x-0 O B. Although lim f(x) exists, it does not equal f(0). X -+ 0 O c. f(0) is not defined. b. Choose the correct answer below. O A. f is not continuous from the left or the right at 0. O B. f is continuous from the left at 0. O C. f is continuous from the right at 0. c. What are the interval(s) of continuity? (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)