165spec1s10

# 165spec1s10 - x 3-4 x 9 x 3 4 6 7 f x =(7 x(1 x 2 8 f x...

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Math 165 Special Assignment I Lowman Spring 2010 Due Thursday, Feb 11 in discussion. The Quiz on Thursday, Feb 11 will be based on this assignment. The general forms (i.e chain rule versions) of the power, log and exponential rules were given in lectures. Part I: 1. List all the rules for ﬁnding limits. 2. List all the rules for ﬁnding derivatives including the general forms of the power rule, log rule and exponential rule. 3. Find the derivative of f ( x ) = 2 x 2 + x by using the limit deﬁnition of the derivative. 4. Find the following limits: (a) lim x 3 2 x +3 x - 3 (b) lim x 3 9 - x 2 x - 3 (c) lim x 3 x - 3 x - 9 (d) lim x →∞ 1 x (e) lim x →-∞ 1 x (f) lim x 0 + 1 x (g) lim x 0 - 1 x (h) lim x 2 (3 x 2 + 2) / ( q (4 x 3 ) + 2 x ) 1

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Part II: Find df dx for the following functions and simplify answers: 1 . f ( x ) = 1 3 x 6 - 2 x 2 + 25 x 2 . f ( x ) = 5 x 4 3 . f ( x ) = 25 x 2 + x 4 . f ( x ) = 1 / ( x 10 ) 5 . f ( x ) = x 2 + 1 / ( x ) 6 . f ( x ) = (6
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Unformatted text preview: x 3-4 x + 9) / ( x 3 / 4 + 6) 7 . f ( x ) = (7 x ) / (1 + x 2 ) 8 . f ( x ) = (1-x 3 ) 4 9 . f ( x ) = (1-5 x 3 ) 1 / 3 10 . f ( x ) = (( x 3-2 x + 1) 2 ) 1 / 3 11 . f ( x ) = q ( x 2-2 x + 1) / (1-x 3 ) 12 . f ( x ) = ((3 x 2 + 5 x ) / (1-5 x 3 )) 4 13 . f ( x ) = a 3 x 3 + a 2 x 2 + a 1 x + a 14 . f ( x ) = ln x 15 . f ( x ) = x ln x 16 . f ( x ) = ln 3 √ x 2 x 4 17 . f ( x ) = ( t + ln t ) 3 / 2 18 . f ( x ) = ln(2 x 2 + 1) 19 . f ( x ) = e x 20 . f ( x ) = e x 2 +1 21 . f ( x ) = e-3 x x 2 +1 22 . f ( x ) = xe 2 x 23. Use implicit diﬀerentiation to ﬁnd dy dx when 20 + 2 x = 4 x 2 + x 3 y 4 24. Use the chain rule to ﬁnd dy dx if y = ( x 2 +2) 3-3( x 2 +2) 2 +1 2...
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## This note was uploaded on 09/09/2010 for the course MATH 165 taught by Professor Staff during the Spring '08 term at Ill. Chicago.

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165spec1s10 - x 3-4 x 9 x 3 4 6 7 f x =(7 x(1 x 2 8 f x...

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