CalculusSummary

# CalculusSummary - CALCULUS SUMMARY A quick reference on...

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Tom Penick www.teicontrols.com/notes 6/11/2001 CALCULUS SUMMARY A quick reference on Exponents, Logarithms, Differentiation, Integration, Power Series Exponents b x 0 b b x y = if and only if x y = b b b x y x y = + ( ) b b x y xy = b b b x y x y / = - a e x x a = ln Logarithms Natural Logarithmic Function f x x x e ( ) log ln = = The natural number e 271828182846 . . To get this number on the calculator, press 1 INV ln x . log e x is written ln x (read "el - en - ex") 1/ 0 lim( 1) x x ex =+ ln x b = if and only if e x b = lim ln x x + = -∞ 0 limln x x →∞ = ∞ . ln e x x = e b a b a ln = ln ln ln xy x y = + ln ln ln x y x y = - ln ln x y x y = Logarithms to other bases : y x a = log if and only if y ax = log log log a a a xy x y = + log log log a a a x y x y = - log log a y a x y x = log log log a b b x x a = A calculator can be used to evaluate an expression such as log 2 14 by virtue of the fact that it is equivalent to ln14/ ln2 . RULES OF DIFFERENTIATION (where u is a function of x ) The derivative of a constant is 0. The power rule: the derivative of n x is 1 n nx - . The general power rule*: d dx n n u nu u = ⋅ ′ - 1 The constant multiple rule: d dx c u c u ( ) = ⋅ ′ The sum and difference rule: d dx u v u v ( ) ± = ′ ± *The General Power rule is a special case of the Chain rule.

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CalculusSummary - CALCULUS SUMMARY A quick reference on...

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