Pre-Calc Homework Solutions 172

Pre-Calc Homework Solutions 172 - 172 Section 4.5 dy dx x2...

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22. (a) Since } d d y x } 5 ( x ) 1 } 2 ˇ 1 w 1 2 w x w 2 w } 2 ( 2 2 x ) 1 ( ˇ 1 w 2 w x w 2 w )(1) 5 } ˇ 1 w 2 2 w x 2 x w 2 w } 1 ˇ 1 w 2 w x w 2 w 5 } 2 x 2 ˇ 1 1 w ( 2 w 1 2 x w 2 w x 2 ) } 5 } ˇ 1 1 w 2 2 w 2 x x w 2 2 w } , dy 5 } ˇ 1 1 w 2 2 w 2 x x w 2 2 w } dx . (b) At the given values, dy 5 } ˇ 1 1 w 2 2 w 2( ( w 0 0 w ) ) 2 2 w } ( 2 0.2) 5 2 0.2. 23. (a) Since } d d y x } 5 e sin x cos x , dy 5 (cos x ) e sin x dx . (b) At the given values, dy 5 (cos p )( e sin p )( 2 0.1) 5 ( 2 1)(1)( 2 0.1) 5 0.1. 24. (a) Since } d d y x } 5 2 3 csc 1 1 2 } 3 x } 2 cot 1 1 2 } 3 x } 21 2 } 1 3 } 2 5 csc 1 1 2 } 3 x } 2 cot 1 1 2 } 3 x } 2 , dy 5 csc 1 1 2 } 3 x } 2 cot 1 1 2 } 3 x } 2 dx . (b) At the given values, dy 5 csc 1 1 2 } 1 3 } 2 cot 1 1 2 } 1 3 } 2 (0.1) 5 0.1 csc } 2 3 } cot } 2 3 } < 0.205525 25. (a) y 1 xy 2 x 5 0 y (1 1 x ) 5 x y 5 } x 1 x 1 } Since } d d y x } 5 } ( x 1 1 ( x )( 1 1) 1 2 ) 2 ( x )(1) } 5 } ( x 1 1 1) 2 } , dy 5 } ( x 1 dx 1) 2 } . (b) At the given values, dy 5 } (0 0 1 .01 1) 2 } 5 0.01. 26. (a) Since } d d y x } 5 sec ( x 2 2 1) tan ( x 2 2 1) ? (2 x ), dy 5 2 x sec ( x 2 2 1) tan ( x 2 2 1 ) dx . (b) At the given values, dy 5 2(1.5) sec (1.5 2 2 1) tan (1.5 2 2 1) ?
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