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Calculus I

by: Ms. Deborah Gaylord

37

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1

Calculus I MATH 1220

Ms. Deborah Gaylord
WMU
GPA 3.59

Niloufer Mackey

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COURSE
PROF.
Niloufer Mackey
TYPE
Class Notes
PAGES
1
WORDS
KARMA
25 ?

Popular in Mathematics (M)

This 1 page Class Notes was uploaded by Ms. Deborah Gaylord on Wednesday September 30, 2015. The Class Notes belongs to MATH 1220 at Western Michigan University taught by Niloufer Mackey in Fall. Since its upload, it has received 37 views. For similar materials see /class/216820/math-1220-western-michigan-university in Mathematics (M) at Western Michigan University.

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Date Created: 09/30/15
Math 1220 THE NUMBER 6 Niloufer Mackey Consider the exponential curves y am7 for di erent values of the base 1 Increase the value of the base from a 2 to a 3 In each case7 we examine the slope of the tangent line to these curves at z 0 These tangent lines all go through the point 017 but with di erent slopes When a 27 the slope is approximately 200001 7 1 W m 69 When a 37 the slope is approximately 300001 7 1 W m 11 Thus7 as the value of the base a continuously increases from 2 to 37 the value of the slope at z 0 increases continuously from about 69 to around 11 By the intermediate value theorern7 there must therefore be a value of the base between 2 and 37 such that the slope at z 0 of the corresponding exponential curve is ewactly equal to 1 This special value of the base is denoted by e The value of 6 lies between 2 and 3 It can be shown that e is not a rational number and its approximate value is 271828

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