# 26 - Limits at Infinity horizontal asymptotes By a limit at...

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Unformatted text preview: Limits at Infinity; horizontal asymptotes By a limit at infinity, we mean "is there a number the function begins to act like as gets large without bound?" denotes "large without bound," while without bound." Consider the function denotes "negatively large What happens to as becomes large without bound, i.e., as the graph and the table, it appears that here, we have Defn: Let lim be a function defined on some interval lim means the values of large values of . and, similarly, Defn: Let can be made arbitrarily close to , then ? From by taking sufficiently be a function defined on some interval lim , then means the values of can be made arbitrarily close to large negatively values of . Defn: The line by taking sufficiently if either is called a horizontal asymptote of lim or lim Now, lim and, lim and, is lim and in general, iIf Thm: If ,what is lim is a rational number, then lim If is a rational number such that lim is defined (real) for all , then lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim lim not an error lim lim cos recall that so what about lim cos ? Since the function continues to oscillate and take on all values between becomes large without bound, this limit does not exist. and as lim arctan arctan lim arctan estimate with graph (1 place) lim b. use table to estimate to 4 places: c. determine exactly lim lim lim lim lim lim which -intercepts: -intercept: lim lim sketch graph using this info: ...
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