371 one to one and increasingdecreasing functions

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Unformatted text preview: One-to-One Function; Inverses cot x dx = ln | sin x| + C , csc x dx = ln |csc x − cot x| + C . logarithmic differentiation (p. 394) 7.4 The Exponential Function one-to-one function; inverse function (p. 371) one-to-one and increasing/decreasing functions; derivatives (p. 374) relation between graph of f and the graph of f −1 (p. 375) continuity and differentiability of inverse functions (p. 375) derivative of an inverse (p. 376) 7.2 The Logarithm Function, Part 1 definition of a logarithm function (p. 381) x dt , x > 0; natural logarithm: In x = t t domain (0, ∞), range (− ∞, ∞) basic properties of ln x (p. 385) graph of y = ln x (p. 385) 7.3 The Logarithm Function, Part II The exponential function y = e x is the inverse of the logarithm function y = ln x. graph of y = e x (p. 398); domain (− ∞, ∞), range (0, ∞) basic properties of the exponential function (p. 398) du du (e ) = e u , dx dx 7.5 eg (x) g (x) dx = eg (x) + C Arbitrary Powers; Other Bases d 1 du (ln |u|) = , dx u dx g (x ) dx = ln |g (x)| + C , g (x ) tan x dx = ln | sec x| + C , sec x dx = ln | sec x + tan x| + C , xr = er ln x for all x > 0, all real r logp x = ln x ln p du du (p ) = pu ln p (p a positive constant), dx dx d 1 du ( logp u) = dx u ln p dx 1+ 1 n n ≤e ≤ 1+ 1 n n+1 e ∼ 2. 71828 =...
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

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