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

1 **Relative rates of Growth**8.3 Relative prices of development

2 fast Review

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4 **What you’ll find out about**Comparing 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.

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

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.

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.

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.

9 **Transitivity of growing Rates**If 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.