CalcNotes0205-page1

CalcNotes0205-page1 - issue is typically required anyway We...

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(Section 2.5: The Indeterminate Forms 0/0 and ± / ± ) 2.5.1 SECTION 2.5: THE INDETERMINATE FORMS 0 0 AND ± ± PART A: WHAT ARE INDETERMINATE FORMS? Roughly speaking, an indeterminate form is a Limit Form that could yield a variety of real values; the limit might not exist. Further analysis is required to know what the limit is. The seven “classic” indeterminate forms are: 0 0 , ± ± , 0 ±² , ±²± , ± 0 , 0 0 , 1 ± Although, for example, the indeterminate form ± ± may be more precisely written as ± ± ± ± , we rarely indicate signs like that, because further analysis beyond the sign
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Unformatted text preview: issue is typically required, anyway. We simply write ± ± out of convenience. Why is an Indeterminate Form? Some examples demonstrate this: lim x ± 2 x x Limit Form ² ³ ´ µ ¶ · = lim x ± 2 = 2 Observe that 2 x x = 2 for all nonzero real values of x , but the limit as x ± does not require 2 x x to be defined for x = . lim x ± ² ³ x x Limit Form ´ µ ¶ · ¸ ¹ = lim x ± ² ( ) = ²...
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