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on an infinite interval. NOTATION: Means that the limit exists and the limit is equal to L. In the example above, the value of y approaches 3 as x increases without %x$. Solution: Since the limit we are asked for is as x approaches negative infinity, we should think of x as a very large negative number. Then %x$ is very large, We read lim x. f x( ) as “the limit of f x( ) as x approaches infinity.” The following rules will help us evaluate “long-run” limits of algebraic functions. Observe that. Name___________________________________. Period____. Date________________. Evaluating Limits. Evaluate each limit. 1) lim x> ?? x + 2 x. 2. + x + x = - p 2 . The graph of f approaches the horizontal line y = p>2 as x S ?, and it approaches the horizontal line y = -p>2 as x S - ?. These lines are called horizontal asymptotes. It is possible for a limit to be both an infinite limit and a limit at infinity. Oct 29, 2015 -Question. Can we describe in mathematics: (1) infinite value of variable? (2) infinite value of function? O f(x)=1/x. 1. 2 Definition. L = lim x>? f(x). ? ?? > 0 ?N > 0 /x>N ? |f(x) ? L| < ? Limit laws do not apply! lim x>0. [1 ? cosx][cotx] ( 0 values of f(x) approach zero. line y = L as x approaches infinity. lim x>??. 2x + 1 x ? 5 . Most of the usual limit laws hold for infinite limits with a replaced by values of f(x) approach zero. line y = L as x approaches infinity. lim x>??. 2x + 1 x ? 5 . Most of the usual limit laws hold for infinite limits with a replaced by Limit at infinity. 12.1. Limit at infinity by inspection. We write limx>? f(x) to represent the height that the graph of f approaches (if any) as x gets ever larger.