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Topic: 1.96 - Can definitions be wrong?
Replies: 2   Last Post: Jul 7, 2014 7:19 PM

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 Dan Christensen Posts: 8,219 Registered: 7/9/08
Re: 1.96 - Can definitions be wrong?
Posted: Jul 7, 2014 3:35 PM

On Monday, July 7, 2014 2:41:39 PM UTC-4, John Gabriel wrote:
> Example for morons:
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> The distance function is given by s(t)= 50t+3.
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> Using the New Calculus, answer the following questions:
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> 1. Find an equation for the speed at any given time t.
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> 2. What can you say about the speed at any given time t?
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> Soln:
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> 1. v(t)=s'(t)= {s(t+n)-s(t-m)}/(m+n) = { 50(t+n)+3 - [50(t-m)+3] } / (m+n)
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> = { 50t+50n+3 - 50t+50m-3 } / (m+n)
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> = 50(m+n)/(m+n)=50
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> So equation for speed at any given time t is: v(t)=50
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> 2. The speed is constant.

v(t) is the first derivative of s(t). Are you now saying that the derivative of a linear function is defined after all?

Dan