Finding Limits Graphically and Numerically

# Finding Limits Graphically and Numerically - bound as x...

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Finding Limits Graphically Section 1.2

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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.
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

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Unformatted text preview: bound as x approaches c . 3. f(x) oscillates between 2 fixed values as x approaches c. Gap in graph Asymptote Oscillates c c c exist not does c x → lim exist not does c x → lim Definition of Limit Let f be a function defined on an open 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 ε δ <-<-< L x f then c x ) ( , L c-L + L + c-c...
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Finding Limits Graphically and Numerically - bound as x...

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