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1.5 Finding Limits Graphically and Numerically

1.5 Finding Limits Graphically and Numerically - interval...

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The Limit of a Function Section 1.5
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To get an idea of the behavior of the graph of f near x = c, you can use 2 sets of x-values –one set that approaches c from the left and another set that approaches c from the right.
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x 1.75 1.9 1.99 2 2.01 2.1 2.2 F(x) 2 2.1 2.19 ? 2.21 2.3 2.4 2 ) ( lim 2 = x f x
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Common Types of Behavior Associated with the Nonexistence of a Limit 1. f(x) approaches a different number from the right side of c than it approaches from the left side. 2. f(x) increases or decreases without bound as x approaches c . 3. f(x) oscillates between 2 fixed values as x approaches c.
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Gap in graph Asymptote Oscillates c c c exist not does c x lim
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Definition of Limit Let f be a function defined on an open
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Unformatted text preview: interval containing c (except possibly at c ) and let L be a real #. means that for each there exists a such that if L x f c x = → ) ( lim ε δ L c ε δ <-<-< L x f then c x ) ( ,-L + L + c-c One-sided and 2-Sided Limits A function f(x) has a limit as x approaches c iff the right-hand and left-hand limits at c exist and are equal lim ( ) lim ( ) lim ( ) x c x c x c If f x L and f x L then f x L +-→ → → = = = Joke Time Why didn’t the quarter roll down the hill with the nickel? Because it had more cents Why didn’t the two 4’s want any dinner? Because they already 8!...
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