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We'll approach this in the traditional way, starting with exponential functions, and defining logarithmic functions from them.

You can always find some sort of inverse RELATION, but in order for a function to have an inverse FUNCTION (a special relation), the original function must be onetoone.  So, we spend some time on these.

7.1 #s 7, 17, 31, 36, 51, 59, 69, 73, 75, 92

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EXAMPLE:

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EXAMPLE

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If time, discuss the geometric argument made in the discussion prior to Theorem 7:

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Attachments

51spread.xlsx

cosineanimationriemann.wmf

51spreadforlecture.xlsx

Sheet1

5.1 #4

nabnab

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SMART Notebook

Area: .9194031702

Partitions: 10

x

0.5

1.0

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0.2

0

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1.0

An Approximation of the Integral of

f(x) = cos(x)

on the Interval [0., 1/2*Pi]

Using a Right-endpoint Riemann Sum

SMART Notebook

Sheet1

5.1 #4

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#8 The region under f(x)=cos(x) from 0 to Pi/2, using n = 10, 30, 50, and 100 rectangles

nabnabnab

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SMART Notebook

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