Question 1 1 pts The following is a graph of a function g(x) , defined on the interval [0 , 4]. g(z) -2 2 3 Choose all the correct statements below. lim g(x) does not exist. O lim g(x) = 2 X2 O lim g(x) does not exist. lim g(xx) - 3 O lim g(x) exists. x-3.5Question 2 1 pts x-a If lim =3 , then what is the value of a ? X - 0 X Your answer should be an integer or a simplified fraction.Question 3 1 pts If lim f (x)-1x1 =4, then what is lim f(x) ? X-3 X2+1 X--3 Your answer should be an integer.Question 4 1 pts Ali, a MAT134 student, writes the following explanation for why the limit lim x . cos( )] is X-0 zero: Since lim x* = 0, we conclude, from the limit laws, that X-0 lim x . cos (3)= lim x4 lim cos 0 X-0 x-0 X-0 X-0 lim cos ( 3x ) = 0 . What is wrong with Ali's explanation? How would you correct it? Upload Choose a FileQuestion 7 1 pts -ax+6 ifx2-1 Let f(x): For what value of a does lim f(x) exist? 2x- tax ifx2 Let f(x) - . Answer the questions below. ax+5 if x52 Show and explain your work. (a) If a-2, what are the one-sided limits lim f(x) and lim f(x) ? -+2 X- 27 (b) Graph the function f(x) for a=2. (c) For what value(s) of a does lim f(x) exist? x- 2 Upload Choose a FileQuestion 9 1 pts Suppose that a function f(x) is discontinuous (i.e., not continuous) at x =c. Then it follows that.. O f(x) is undefined at x =c. O lim f(x) does not exist. O f(x) has a denominator that is equal to zero when x = c . Of(c) and lim f(x ) are different, if they both exist.\fQuestion 11 1 pts Answer the following questions. Show and explain your work. (a) What type of discontinuity does the function g(x) = have at x =0 ? Explain. el/x - 1 (b) For which value of c will the function f(x) = el/x _ 1 +c ) have a limit at x =0 ? Hint: Use one-sided limits.) (c) Using the value for c found in part (b), how would you define / (x) at x =0 so that / becomes continuous at x=() ? Explain