Transcription of Harold’s Calculus Notes Cheat Sheet - Toomey
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Harold’s Calculus Notes Cheat Sheet - Toomey
harold 's Calculus Notes Cheat Sheet 4 April 2020. AP Calculus Limits Definition of Limit Let f be a function defined on an open interval containing c and let L be a real number. The statement: lim ( ) = .. means that for each > 0 there exists a > 0 such that if 0 < | | < , then | ( ) | < . Tip : Direct substitution: Plug in ( ) and see if it provides a legal answer. If so then L =. ( ). The Existence of a Limit lim ( ) = .. The limit of ( ) as approaches a is L if lim ( ) = . and only if: +.. Prove that ( ) = is a continuous function. | ( ) ( )|. Definition of Continuity = |( 2 1) ( 2 1)|. = | 2 1 2 + 1|. A function f is continuous at c if for = | 2 2 |. every > 0 there exists a > 0 such that = |( + )( )|. | | < and | ( ) ( )| < . = |( + )| |( )|. Since |( + )| |2 |. Tip: Rearrange | ( ) ( )| to have | ( ) ( )| |2 ||( )| < .. |( )| as a factor. Since | | < we So, given > 0, we can choose = | | > in the . can find an equation that relates both Definition of Continuity.
Harold’s Calculus Notes Cheat Sheet 4 April 2020 AP Calculus Limits Definition of Limit Let f be a function defined on an open interval containing c and let L be a real number. The statement: lim
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