lecture23hout

# lecture23hout - MATH 006 Calculus and Linear...

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Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 23) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 13 Outline 1 Related Rates Albert Ku (HKUST) MATH 006 2 / 13 Related Rates Related Rates Given two quantities x and y , which are related by an equation. Suppose these quantities are also dependent on time t i.e. x = x ( t ) and y = y ( t ). Then from the given equation we can derive another equation which involves dx dt and dy dt . These are called the related rates . The equation about the related rates can be obtained by differentiating both sides of the given equation with respect to t . The technique is very similar to implicit differentiation. Albert Ku (HKUST) MATH 006 3 / 13 Related Rates Example A 26-foot ladder is placed against a vertical wall. If the top of the ladder is sliding down the wall at 2 feet per second, at which rate is the bottom of the ladder moving away from the wall when the bottom of the ladder is 10 feet from the wall? Albert Ku (HKUST) MATH 006 4 / 13 Related Rates Solution First, we let x be the distance from the wall to the bottom of the ladder and y be the distance from the floor to the top of the ladder. Then bybe the distance from the floor to the top of the ladder....
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lecture23hout - MATH 006 Calculus and Linear...

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