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Use the graph of the greatest integer function, y = LxJ, to nd the limits given below. (3) lim % (1)) lim % e>2* e> 2' (a) Select the correct choice below and ll in any answer boxes within your choice. 9 O A. Iim % = (Type an integer or a simplied fraction.) 9 2' O 3_ The limit does not exist. (b) Select the correct choice below and ll in any answer boxes within your choice. 7 = (Type an integer or a simplied fraction.) Which of the statements a through k about the function y = f(x) graphed here are true, and which are false? a. The statement Iim f(x) exists is y ' x>0 4 y Q h. The statement Iim f(x) =2 is V O\\ x>0 - H c. The statement Iim f(x) =0 is V x>0 x :2 > 4 d. The statement Iim f(x) =2 is v x>2 e. The statement Iim f(x) = 2 is V x>2 4 f. The statement Iim f(x) exists at every point e in (2,2) is xn: g. The statement Iim f(x) does not exist is V x>2 h. The statement f(0) =2 is V i. The statement f(0) = O is V j. The statement f(2) = 2 is V k. The statement f(2) = - 2 is V Suppose that lim f(x) = 13 and lim g(x) = -5. Find the following limits. x-b x-b f(x ) a. lim (f(x) + g(x)) b. lim 8g(x) c. lim f(x) .g(x) d. lim x-+b x-+b x-b x-+b g(x) a. lim (f(x) + g(x)) = (Simplify your answer.) x-b b. lim 8g(x) = (Simplify your answer.) x-b c. lim f(x) . g(x) = (Simplify your answer.) x-b f(x) d. lim S (Type an integer or a simplified fraction.) x-+b 9(x)Suppose that a function f(x) is defined for all real values ofx except atx = c. Can anything be said about the existence of lim f(x)? Give reasons for your answer. X>C C'- A. At x = 6, lim f(x) exists, and its value is the average of the values obtained as x approaches c from the right and from the left. XJ-C '1:- B. At x = c, lim f(x) does not exist because the function is undened at the point x= c. X)C '1:- C. At x = c, lim f(x) does not exist because it is likely that the function oscillates orjumps at that point. X>C C" D. Nothing can be said about the existence Of the limit. The function might approach the same value from both sides. or it might jump or oscillate as XNG