Question 1. (1) Write a proof for the following Theorem: Theorem Let {an}o be a sequence. Let LE R. Let f be a function. {an}n=0 IF {an} n=0 L f is continuous at L THEN {f(an)}no (L) . n= To help you write a correct proof: (a) Write the definition of your hypotheses and your conclusion. (b) Using the definition of your conclusion, figure out the structure of the proof. (c) Do some rough work if necessary. (d) Write a formal proof. (2) Compute the following limits (no need to justify your answer): (a) lim n (b) lim n! + 2en 3n! + 4en 2n + (2n) n 2n+1 + n (c) lim 5n5+5+5n! n nn