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# M2-Ch4 - M2 M2 Calculus Fall 2011 Review Ch1 Y = mX b m1 =...

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M2 M2 Calculus Fall 2011

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Review Ch1 i x a x a iff a x < < - < | | a x or x a iff a x < - | | ) ( x f y = ) ( ) ( x f x f - = - ) ( ) ( x f x f = - b mX Y + = 1 2 1 2 x x y y x y m - - = = x y b 1 2 1 - = m m 2 1 m m =
Review Ch1 Composition: Example: )) ( ( ) )( ( x g f x g f = x x x g x x f + - = = 1 1 ) ( sin ) ( ) 1 1 sin( ) 1 1 ( )) ( ( ) )( ( x x x x f x g f x g f + - = + - = = x x x g x f g x f g sin 1 sin 1 ) (sin )) ( ( ) )( ( + - = = = t t t t f g t g f sin 1 1 ) )( ( ) )( ( + - = = t t t t f g t g f sin 1 1 ) )( ( ) )( ( + + - = + = +

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Limits 1. Left hand limit 2. Right hand limit 3. Limit Limits and Continuity Chapter 2 Continuity If Then L x f c x = - ) ( lim M x f c x = + ) ( lim Exists x f c x = ) ( lim M L x f c x M L iff = = = ) ( lim Exists x f c x = ) ( lim ) ( ) ( lim c f x f c x and = c x at continuous is x f = ) ( exist not does it the M L If lim ,
Rules 1. Limit Limits and Continuity Chapter 2 Continuity 1. If 2. Then ) ( lim ) ( lim )] ( ) ( lim[ x g x f x g x f + = + Exists x f c x = ) ( lim ) ( ) ( lim c f x f c x and = c x at continuous is x f = ) ( )] ( )][lim ( [lim )] ( ) ( lim[ x g x f x g x f = ) ( lim )] ( lim[ x f k x kf = M x f c x then M x f c x if 1 ) ( 1 lim ) ( lim = =

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Limits and Continuity Chapter 2 Find the limits using the Graph 4 1 -
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M2-Ch4 - M2 M2 Calculus Fall 2011 Review Ch1 Y = mX b m1 =...

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