Calc08_2day2 - is indeterminate 0.1 lim x x-→∞ =...

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8.2 Day 2: Identifying Indeterminate Forms Brooklyn Bridge, New York City Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2008
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What makes an expression indeterminate? lim 1000 x x →∞ = ∞ Consider: We can hold one part of the expression constant: 1000 lim 0 x x →∞ = There are conflicting trends here. The actual limit will depend on the rates at which the numerator and denominator approach infinity, so we say that an expression in this form is indeterminate .
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Let’s look at another one: 0 0 lim1000 1 x x = Consider: We can hold one part of the expression constant: 0.1 lim x x →∞ = ∞ Once again, we have conflicting trends, so this form
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Unformatted text preview: is indeterminate . 0.1 lim x x-→∞ = Finally, here is an expression that looks like it might be indeterminate : ∞ ( 29 lim .1 x x →∞ = → Consider: We can hold one part of the expression constant: ( 29 lim .1 x x →∞-= The limit is zero any way you look at it, so the expression is not indeterminate . 1000 lim x x → = Here is the standard list of indeterminate forms: ∞ ∞ ∞⋅ ∞ - ∞ 1 ∞ ∞ There are other indeterminate forms using complex numbers, but those are beyond the scope of this class. π...
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Calc08_2day2 - is indeterminate 0.1 lim x x-→∞ =...

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