2.7 Rates of Change in the Natural and Social Sciences

2.7 Rates of Change in the Natural and Social Sciences - v...

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Rates of Change in the Natural and Social Sciences Section 2.7
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Instantaneous Rate of Change v The instantaneous rate of change of f with respect to x at a is the derivative provided the limit exists. ( ) ( ) ( ) lim h o f a h f a f a h + - =
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Average Velocity t s time in change distance in change =
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Speed v The speed of an object is the absolute value of its velocity. Speed cannot be negative. v Speed = ( ) ds v t dt =
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Free-fall Constants (Earth) English units: Metric units: 2 2 2 1 32 , (32) 16 ( ) sec 2 ft g s t t s in feet = = = 2 2 2 1 9.8 , (9.8) 4.9 ( ) sec 2 m g s t t s in meters = = =
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v (s) t is the position function
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Unformatted text preview: v (v) t is the velocity function and is the first derivative of the position function. v (a) t is the acceleration function and is the first derivative of velocity or the second derivative of the position function. ( ) ( ) ( ) ( ) ( ) ( ) s t v t s t a t v t s t = = = Economics Joke Time v How does a lion greet the other animals in the jungle? v Pleased to eat you. v What happened when the lion ate the comedian? v He felt funny!...
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2.7 Rates of Change in the Natural and Social Sciences - v...

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