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Unformatted text preview: y = ln F ( x ), • using the Laws of Logarithms to simplify the new equation, 1 • diﬀerentiating the equation implicitly with respect to x , • solving the resulting equation for y . The Laws of Logarithms : Given a > , a 6 = 1, x and y are positive numbers, then • 1. log a ( xy ) = log a x + log a y • 2. log a ( x y ) = log a xlog a y • 3. log a ( x r ) = r log a x Example 7 of Section 3.6 (textbook): Example 8 of Section 3.6 (textbook): The Number e as a Limit In Section 3.1, we learned that: if f ( x ) = a x ( a > , a 6 = 1) then e is the number such that f (0) = lim h → e h1 h = 1. Reminder : The geometric meaning of the slopes f (0) of the exponential function f ( x ) = a x In this section, e can be rigorously deﬁned as e = lim x → (1 + x ) 1 x (check the proof on page 219 of the textbook). From the above graph and table, e ≈ 2 . 7182818. 2...
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 Fall '08
 Noohi
 Calculus, Exponential Function, Chain Rule, Derivative, Exponential Functions, Logarithmic Functions, The Chain Rule, Natural logarithm, Ms. Hoa Nguyen

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