Review_Slides_22_Apr_

Review_Slides_22_Apr_ - AP Calculus AB Exam Review LIMITS...

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AP Calculus AB xam Review Exam Review
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LIMITS
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Finding Limits Substitute a for x and simplify c b a constant (including 0) is the limit ndefined check for INFINITE LIMIT ( ) x f a x lim c / 0 b undefined ; check for INFINITE LIMIT 0 / 0 b indeterminate ; DO SOMETHING ELSE factor and cancel simplify rationalize radicals L’Hospital’s Rule Confirm that LHL = RHL
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Finding Limits Only highest-power terms are significant ( ) x f x lim ( ) x f x -∞ lim Simplify if result is constant, the constant is the limit if top degree > bottom degree, limit is ±∞ if bottom degree > top degree, limit is 0 Watch out for negative exponents!
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continuity A function is continuous at x = c iff f ( c ) exists ists (LHL = RHL) m exists (LHL = RHL) ( ) x f c x lim ( ) x f c f c x = lim ) (
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I V T Intermediate Value Theorem IF a function is CONTINUOUS on [ a , b ] AND there is a value y between f ( a ) and f ( b ), THEN there is a value c on ( a , b ) such that f ( c ) = y .
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E V T Extreme Value Theorem IF a function is CONTINUOUS on [ a , b ], THEN there exist values c (max) and d (min) on [ a , b ] such that f ( c ) f ( x ) f ( d ).
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Derivative as a Limit A limit in this form equals f '( x ) ( ) h x f h x f h ) ( lim 0 - + identify the function f and differentiate substitute a given constant for x , if applicable
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DERIVATIVES
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Definitions of Derivative Derivative at a Point x = c c x c f x f c f c x - - = ) ( ) ( lim ) ( ' Derivative Function ( ) h x f h x f x f h ) ( lim ) ( ' 0 - + =
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Derivative of a Function Instantaneous RATE OF CHANGE Slope of the Tangent Line Estimate a derivative using the AVERAGE Rate of Change, or Slope of the Secant Line
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To find the equation of a tangent line, you need: a POINT ( x 1 , y 1 ) identify x 1 (usually given) find y 1 using f ( x 1 ) the SLOPE take the derivative
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Review_Slides_22_Apr_ - AP Calculus AB Exam Review LIMITS...

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