Please provide clear explanations for these questions. Thank you so much.

Answer the following questions. Show and explain your work. (a) What type of discontinuity does the function g ( x ) = - el/x - 1 have at x=0 ? Explain. (b) For which value of C will the function f (x) = ( el/x - +c ) have a limit at x=0 ? (Hint: Use one-sided limits.) (c) Using the value for found in part (b), how would you define f(x) at x=0 so that becomes continuous at x=0 ? Explain.The following is a graph of a function g (x ) , defined on the interval [0 , 4] Choose all the correct statements below. O lim g(x) x-1 does not exist. O lim g(x) = 2 x-3 O lim g(x) x-2 does not exist. O lim g(x) = 3 O lim g(x) exists.Let f ( x ) = 1 x ta ifx >2 ax+5 if x52 . Answer the questions below. Show and explain your work. (a) If a=2 , what are the one-sided limits lim f(x) x-2 and lim f(x) x - 2+ . V (b) Graph the function f(x) for a=2 (c) For what value(s) of a does lim f(x) x-2 exist