Pre-Calc Homework Solutions 337

Pre-Calc Homework Solutions 337 - Section 8.3 dx(1 x 1 2...

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17. First integrate E } (1 1 d x x ) ˇ x w } by letting u 5 ˇ x w , so du 5 } 2 ˇ 1 x w } dx . E } (1 1 d x x ) ˇ x w } 5 E } 1 2 1 du u 2 } 5 2 tan 2 1 u 1 C 5 2 tan 2 1 ˇ x w 1 C Now evaluate the improper integral. Note that the integrand is infinite at x 5 0. E 0 } (1 1 d x x ) ˇ x w }5 E 1 0 } (1 1 d x x ) ˇ x w }1 E 1 } (1 1 d x x ) ˇ x w } 5 lim b 0 1 E 1 b } (1 1 d x x ) ˇ x w lim c E c 1 } (1 1 d x x ) ˇ x w } 5 lim b 0 1 3 2 tan 2 1 ˇ x w 4 1 lim c 3 2 tan 2 1 ˇ x w 4 5 lim b 0 1 (2 tan 2 1 1 2 2 tan 2 1 ˇ b w ) 1 lim c (2 tan 2 1 ˇ c w 2 2 tan 2 1 1) 5 1 } p 2 } 2 0 2 1 1 p 2 } p 2 } 2 5 p 18. E 1 } x ˇ x d 2 w x 2 w 1 w } 5 E 2 1 } x ˇ x d 2 w x 2 w 1 w E 2 } x ˇ x d 2 w x 2 w 1 w } E 2 1 } x ˇ x d 2 w x 2 w 1 w } 5 lim b 1 1 E 2 b } x ˇ x d 2 w x 2 w 1 w } 5 lim b 1 1 3 sec 2 1 x 4 5 lim b 1 1 (sec 2 1 2 2 sec 2 1 b ) 5 sec 2 1 2 2 sec 2 1 1 5 } p 3 } E 2 } x ˇ x d 2 w x 2 w 1 w } 5 lim b E b 2 } x ˇ x d 2 w x 2 w 1 w } 5 lim b 3 sec 2 1 x 4 5 lim b (sec 2 1 b 2 sec 2 1 2) 5 } p 2 } 2 } p
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