Chap2_Sec7

Chap2_Sec7 - TANGENTS Let Q approach P along the curve C by...

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Let Q approach P along the curve C by letting x approach a . s If m PQ approaches a number m , then we define the tangent t to be the line through P with slope m . s This m amounts to saying that the tangent line is the limiting position of the secant line PQ as Q approaches P . TANGENTS
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Notice that, as x approaches a , h approaches 0 (because h = x - a ). s So, the expression for the slope of the tangent line becomes: 0 ( ) ( ) lim h f a h f a m h + - = TANGENTS 2. Definition
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Find an equation of the tangent line to the hyperbola y = 3/ x at the point (3, 1). TANGENTS Example 2 (2.7)
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Suppose that a ball is dropped from the upper observation deck of the CN Tower, 450 m above the ground. a. What is the velocity of the ball after 5 seconds? b. How fast is the ball traveling when it hits the ground? VELOCITIES Example 3 (2.7)
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In fact, limits of the form arise whenever we calculate a rate of change in any of the sciences or engineering— such as a rate of reaction in chemistry or a marginal cost in economics. The derivative of a function
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Chap2_Sec7 - TANGENTS Let Q approach P along the curve C by...

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