Answer the following questions. Show and explain your work. 1 (a) What type of discontinuity does the function g(:I:) : have at a: : 0 ? Explain. 31/931 1 2 lc have a limit at $20 ? 31/'31 (b) For which value of c will the function gs) 2 ( (Hint: Use one-sided limits.) (C) Using the value for c found in part (b), how would you dene f(:I:) at :12: 0 so that f becomes continuous at :13: 0 ? Explain. Ali, a MAT134 student, writes the following explanation for why the limit lim ac . cos ( is zero: Since lim x4 = 0, we conclude, from the limit laws, that lim [a 4 . cos ( 3 ) ] = lim x 4 lim cos 3x = 0. lim cos 3x = 0 . x-70 What is wrong with Ali's explanation? How would you correct it?3:2 +0, if a: > 2 _ Let m) = . Answer the questions below. as: +5 if a: g 2 Show and explain your work. (a) If (:22, what are the one-sided limits 11m x) and ' f(l':)? 2 mk2' $> + (b) Graph the function rs) for (122. (c) Forwhat value(s) of a does ling f(:1:) exist? 32}