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Unformatted text preview: Problem Set 7 Calculus 1 Abdullah Khalid, Hassan Bukhari January 3, 2010 Announcement: I am available all day Tuesday to ask questions. Please feel free to drop by in the office any time. 1. Apply the Mean Value Theorem to the function f on the interval (- b,b ) to find a point c such that f ( c ) = f ( b )- f (- b ) 2 b Since f is odd, f ( b ) =- f (- b ). Hence f ( c ) = f ( b ) /b . 2. (a) Applying L’Hospital’s rule we get lim x →∞ ln ln x x = lim x →∞ 1 x ln x = 0 (b) The limit does not exist. A very intuitive reason why the limit does not exist is because sin oscillates between -1 and 1 where as ln x approaches ∞ as x approaches ∞ . (c) We know that lim x → + x ln x = lim x → + ln x x- 1 = lim x → +- x 2 x = lim x → +- x = 0 So we can rewrite lim x → + sin x ln x = lim x → + sin x x x ln x = lim x → + sin x x lim x →∞ x ln x = 0 1 (d) We want to find lim x →∞ f ( x ) where f ( x ) = x 1 /x . Let us first compute the limit of ln f ( x ). lim x →∞ ln f ( x ) = lim x →∞ ln x x = 0 where the last equality follows by a simple application of L’Hospital’s rule....
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This note was uploaded on 01/10/2011 for the course EE 100 taught by Professor Razasuleman during the Spring '10 term at University of Engineering & Technology.
- Spring '10