161-f11-sg3 - Fall 2011 MA 16200 Study Guide - Exam # 3 (1)...

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Unformatted text preview: Fall 2011 MA 16200 Study Guide - Exam # 3 (1) Method to solve Related Rates problems: 1 Read problem carefully several times 2 Draw a picture (if possible) and label. 3 Write down given rate; write down desired rate. 4 Find an equation relating the variables. 5 Use Chain Rule to differentiate equation w.r.t to time and solve for desired rate. (2) The linear approximation (or tangent line approximation) to a function f ( x ) at x = a is L ( x ) = f ( a ) + f ( a )( x a ); Approximation formula : f ( x ) f ( a ) + f ( a )( x a ) , for x near a ; if y = f ( x ), the differential of y is dy = f ( x ) dx . (3) Hyperbolic Trig Functions (a) Definitions: (i) cosh x = e x + e x 2 (ii) sinh x = e x e x 2 (iii) tanh x = sinh x cosh x = e x e x e x + e x (b) Derivatives: (i) (cosh x ) = sinh x (ii) (sinh x ) = cosh x (iii) (tanh x ) = sech 2 x (c) Basic Identites: (i) cosh ( x ) = cosh x (ii) sinh ( x ) = sinh x (iii) cosh 2 x...
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161-f11-sg3 - Fall 2011 MA 16200 Study Guide - Exam # 3 (1)...

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