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Review Sheet 1205 Test 2
1. Derivatives:
l' (x) = lim J(x + h) - J(x) if the limit exists.
h-->O h
We evaluated this limit in several ways:
tables
reading from the graph
defmition
rules
~ A function is differentiable if the derivative exists.
A derivative does not exist:
at a corner or sharp peak
where there is a vertical tangent
at a discontinuity
~ Iff is differentiable at c then f is continuous at c.
Section 2.8 - 3.7, Worksheets 3-6
Since this limit is a rate of change it can give us instantaneous velocity:
If s = J(t) is the position fctn with respect to time, then
. J(t + At) - j(t). .
v(t) = S' (t) = hm IS velOCIty
M-V I1t
speed = Iv(t) I
a( t) = v' (t) is acceleration ~'-__ " I (~')
We can use this information in many ways:
Make decisions like the following:
particle is momentarily at rest (that is, changing directions) when s'C t) = 0
particle is moving to the right when s'C t) +
particle is moving to the left whens'(t)-
particle is speeding up w...

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