Question: 1) Prove the following statement using the e- definition of limits: If lim f(x) = 4, then lim (f(x)-3f(x) + 4) = 8. I

1) Prove the following statement using the e- definition of limits: "If lim f(x) = 4, then lim (f(x)-3f(x) + 4) = 8." I I 7 Be sure to justify your choice of constants. Do not use theorems from the course to evaluate the limit - you MUST use the definition! 2) Let a R and define fa(r) = = 1 ar + ar 6 (a) Find all values of a (if they exist) such that fa(r) has a horizontal asymptote at y = . (b) Find all values of a (if they exist) such that fa(r) has a vertical asymptote at x = -2. (c) Find all values of a (if they exist) such that fa(r) is continuous everywhere.

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