Question

Please do not write in cursive, as I cannot read cursive. Please explain how you got the answers and show the work. Thank you very much

in-too An does not? 1) Could there be a sequence {an}= {f (n)} such that limita—700 f (x) exists, but limit 2) Could limit noo An exists but not for limitx-700 f(x) 3) Discuss your options , you can give an example to enhance your reasoning.

Answer 1

No, rzo let lim flo a So, given any that for there exists such X ER any 1260) - ll< take for nola, then any I f(n) -elce of n zno lim fin 9 Hence, lima, & can) exists Yes Define 26t-n) tent/ fl) nt Al -2 (x=(n+1)) :nth : nt1 ce nt! le goaxis] Graph of f(x) H 2.

then for Ony natural So lim fin) exists & w does not exist x > 0 as Bast Since, as nt 1 2 1 then f (n+1) But as then Hence, to tas twe sequences infinity with different lim fo does not exist going limits So