2areview - MATH 2A REVIEW Midterm 1 sin(2 x h sin(2 x lim equals h!0 h A = 2cos(2x B = zero C Does not exist because 0/0 is undefined Recall the

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MATH 2A REVIEW - Midterm 1-
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lim h ! 0 sin(2 x + h ) " sin(2 x ) h equals A) = 2 cos (2x) B) = zero C) Does not exist because 0/0 is undefined.
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f '( x ) = lim h ! 0 f ( x + h ) " f ( x ) h Recall the definition of derivative as a limit of the difference quotient (when this limit exists). If the problem explicitly says find the derivative of f using the definition then you must take this kind of limit… In all other cases you can use the Differentiation rules!
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use the chain rule and power rule
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The proof follows from the chain rule: OK
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use chain rule and deriv of trig
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derivative of outer function evaluated at inner function derivative of inner function OK
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use the product rule and chain rule
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chain rule OK Product rule
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use the definition of countinuity and a limit by rationalization
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f is defined at 0, and equal to 1/2. f is continuous at 0 iff the limit of f for x 0 is equal to 1/2 lim x ! 0 x 2 + 1 " 1 x 2 = lim x ! 0 x 2 + 1 " 1 x 2 x 2 + 1 + 1 x 2 + 1 + 1 = = lim x ! 0
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This note was uploaded on 12/07/2010 for the course MATH MATH 2A taught by Professor Alessandrapantano during the Fall '10 term at UC Irvine.

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2areview - MATH 2A REVIEW Midterm 1 sin(2 x h sin(2 x lim equals h!0 h A = 2cos(2x B = zero C Does not exist because 0/0 is undefined Recall the

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