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Unformatted text preview: CALCULATING LIMITS USING THE LIMIT LAWS Limit Laws Suppose that c is a constant and the limits lim x → a f ( x ) and lim x → a g ( x ) exist. Then, 1 . lim x → a [ f ( x ) + g ( x )] = lim x → a f ( x ) + lim x → a g ( x ) 2 . lim x → a [ f ( x ) g ( x )] = lim x → a f ( x ) lim x → a g ( x ) 3 . lim x → a [ cf ( x )] = c lim x → a f ( x ) 4 . lim x → a [ f ( x ) g ( x )] = lim x → a f ( x ) · lim x → a g ( x ) 5 . lim x → a f ( x ) g ( x ) = lim x → a f ( x ) lim x → a g ( x ) if lim x → a g ( x ) 6 = 0 6 . lim x → a [ f ( x )] c = h lim x → a f ( x ) i c If f is a polynomial or a rational function and a is in the domain of f , then lim x → a f ( x ) = f ( a ) . We call this Direct Substitution Property , and functions with the Direct Substitution Property are called continuous at a . By using this property and the limit laws, we can compute most of limit problems....
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This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.
 Fall '09
 BenedictGross
 Limits

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