CalcNotes0202-page2 - ( ) , or lim x a cf x ( ) = c lim x a...

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(Section 2.2: Properties of Limits and Algebraic Functions) 2.2.2 5) The limit of a power equals the power of the limit. If n is a positive integer, then: lim x ± a fx () ² ³ ´ µ n = lim x ± a fx () ² ³ ´ µ · n = L 1 () n 6) The limit of a root equals the root of the limit. If n is a positive integer, and either • ( n is odd), or • ( n is even, and L 1 > 0 ), then: lim x ± a fx () n = lim x ± a fx () n = L 1 n (We will discuss related examples later.) 7) The limit of a constant multiple equals the constant multiple of the limit (“Constant Factors Pop Out.”) If c is a real constant, then: lim x ± a c ² fx
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Unformatted text preview: ( ) , or lim x a cf x ( ) = c lim x a f x ( ) = cL 1 (For more on Properties 5 and 6, see Footnote 6 in Section 2.8.) Limit Operators are Linear Properties 1), 2), and 7) imply that limit operators are linear. This means that we can take limits term-by-term, and then constant factors pop out, assuming the limits exist. (See Footnote 1.) This is a key general property that is shared by the differentiation and integration operators we will discuss in later chapters....
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

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