1007_Tut3

# 1007_Tut3 - f ( x ) = 0 or f ( x ) DNE. Hint: Show that x =...

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MATH 1007 A Tutorial #3 Oct 27, 2006 First Name: Last Name: Student No: No Calculators! You must show your work for all questions! 1. [3 marks] Find the most general antiderivative: (a) f ( x ) = 4 + x 2 - 5 x 3 (b) g ( x ) = x 20 + 4 x 10 + 8

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3. [7 marks] Let y = f ( x ) = x (ln x ) 2 . Note that the domain of f is (0 , ) since ln x is only deﬁned for x > 0. The following approximate values may be useful e 2 . 718 e 2 7 . 389 1 e 0 . 368 1 e 2 0 . 135 4 e 2 0 . 541 Please answer ALL of the following questions: (separate sheet provided) (a) Find the x intercept(s) (set y = 0). [Note: there is no y intercept.] (b) Evaluate lim x →∞ f ( x ) to see what happens when x is large. (c) Evaluate lim x 0+ f ( x ) to see what happens near 0. Hint: Write f = x (ln x ) 2 = (ln x ) 2 1 /x and apply l’hopital’s rule twice to simplify. (d) Find f 0 ( x ), and ﬁnd all values with
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Unformatted text preview: f ( x ) = 0 or f ( x ) DNE. Hint: Show that x = 1 and x = e-2 are the only critical values of f . (e) Give a table of intervals of increase and decrease for f . (f) Give the x and y coordinates of any local maximums and minimums. (g) Find f 00 ( x ), and ﬁnd all values with f 00 ( x ) = 0 or f 00 ( x ) DNE. Hint: Show that x = e-1 is the only possible point of inﬂection of f . (h) Give a table of intervals of concavity of f . (i) Give the x and y coordinates of any points of inﬂection of f . (j) Using all the information given, and your solutions from (a) to (i), sketch the graph of the function f ....
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## This note was uploaded on 03/22/2010 for the course MATH 1007 taught by Professor Unknown during the Fall '07 term at Carleton.

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1007_Tut3 - f ( x ) = 0 or f ( x ) DNE. Hint: Show that x =...

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