Presentation on theme: "Relative rates of Growth"— Presentation transcript:

1 Relative rates of Growth8.3 Relative prices of development

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2 fast Review

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4 What you’ll find out aboutComparing prices of development Using L’Hôpital’s dominion to Compare growth Rates Sequential versus Binary Search important Question exactly how do we usage calculus to understand development rates together x→∞ and how it helps us know the behavior of functions.

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5 Faster, Slower, Same-rate expansion as x→∞Let f (x) and also g (x) be confident for x sufficiently large, 1. F grows much faster than g (and g grows slower than f ) together x → ∞ if 2. F and also g flourish at the same rate as x → ∞ if

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6 Example compare ex and also x3 as x→∞Show that e x grows quicker than x 3 together x → ∞. The border is of the indeterminate form ∞/ ∞, so us can use L’Hôpital’s Rule.

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7 Example to compare ln x v x together x→∞Show the ln x grow slower 보다 x together x → ∞. The limit is that the indeterminate type ∞/ ∞, so we can apply L’Hôpital’s Rule.

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8 Example comparing x through x + sin x together x→∞Show the x grows at the same price as x + sin x together x → ∞. The border is the the indeterminate type ∞/ ∞, so we can use L’Hôpital’s Rule.

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9 Transitivity of growing RatesIf f grow at the same rate as g together x → ∞ and also g grows at the same rate as h as x → ∞, climate f grows at the same price as h together x → ∞.


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10 Example farming at the Same price as x→∞Show that f and g flourish at the same price by reflecting that they both thrive at the same rate as h(x) = x.

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