Chapter 9.1, Problem 59E

EVALUATE LIMIT

Definition Let . We say that  is the limit of  f as x->∞ and write limx->∞f(x)=L provided that for each episilon greater than 0 there is a real number N>a such that x>N implies that |f(x)-L|<episilon   Use the above definition to prove the following: Let f and g be real-valued functions defined on (b, ∞). Suppose that limx->∞f(x)=L and limx->∞g(x)=M, where L, M ∈ ℝ . Prove the following  If  g(x) is not 0 for  x>a and M is not 0 , then limx->∞(f/g)(x)=L/M

Evaluating a limit.

Find the limit (if it exists) lim x →3 x²-9/ 27-x²

ILLUSTRATION OF LIMIT THEOREMS Complete the following table : lim 2001 lim x lim f(x)=5 7 13 2.33 9 11.5 Assume the following : lim f (x) =4 lim g(x) = 10 JーX lim h(x) = -3 SHOW YOUR SOLUTION 1.lim(7 · f (x))= X→C 2.lim /12 · f(x) x→c 3.lim(f(x) – h(x)) 4.lim f (x) · g(x) g(x)+h(x) 5.lim f(x)

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Question Calculate the limit. If the limit does not exist, enter Ø. lim n→∞ (n+8)!] n+∞|(n+2)! Provide your answer below: (n+8)! (n+2)! lim = : SUBMIT