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161-f11-sg3

# 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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