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Pre-Calc Homework Solutions 234

Pre-Calc Homework Solutions 234 - 234 Section 6.1 dy dx dy...

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24. E cot 2 t dt 5 E (csc 2 t 2 1) dt 5 2 cot t 2 t 1 C 25. (a) Graph (b) (b) The slope is always positive, so (a) and (c) can be ruled out. 26. (a) Graph (b) (b) The solution should have positive slope when x is negative, zero slope when x is zero and negative slope when x is positive since slope 5 } d d y x } 5 2 x . Graphs (a) and (c) don’t show this slope pattern. 27. } d d y x } 5 2 x 2 1 E } d d y x } dx 5 E (2 x 2 1) dx y 5 x 2 2 x 1 C Initial condition: y (2) 5 0 0 5 2 2 2 2 1 C 0 5 2 1 C 2 2 5 C Solution: y 5 x 2 2 x 2 2 [ 2 4, 4] by [ 2 3, 3] 28. } d d y x } 5 } x 1 2 } 1 x E } d d y x } dx 5 E ( x 2 2 1 x ) dx y 5 2 x 2 1 1 } x 2 2 } 1 C y 5 } x 2 2 } 2 } 1 x } 1 C Initial condition: y (2) 5 1 1 5 } 2 2 2 } 2 } 1 2 } 1 C 1 5 } 3 2 } 1 C 2 } 1 2 } 5 C Solution: y 5 } x 2 2 } 2 } 1 x } 2 } 1 2 } [ 2 6, 6] by [ 2 4, 4] 29. } d d y x } 5 sec 2 x E } d d y x } dx 5 E sec 2 x dx y 5 tan x 1 C Initial condition: y 1 } p 4 } 2 5 2 1 2 1 5 tan } p 4 } 1 C 2 1 5 1 1 C 2 2 5 C Solution: y 5 tan x 2 2 3 2 } p 2 } , } p 2 } 4 by [ 2 8, 8] 30.
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