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Pre-Calc Homework Solutions 114

# Pre-Calc Homework Solutions 114 - 114 Section 3.8 22...

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22. continued (c) At the points x 5 k } p 2 } , where k is an odd integer. (d) (e) f 9 ( x ) 5 } d d x } sin 2 1 (sin x ) 5 } ˇ 1 w 2 w 1 s w in w 2 w x w } } d d x } sin x 5 } ˇ 1 w c 2 w os s w x in w 2 w x w } which is 6 1 depending on whether cos x is positive or negative. 23. (a) v ( t ) 5 } d d x t } 5 } 1 1 1 t 2 } which is always positive. (b) a ( t ) 5 } d d v t } 5 2 } (1 1 2 t t 2 ) 2 } which is always negative. (c) } p 2 } 24. } d d x } cos 2 1 ( x ) 5 } d d x } 1 } p 2 } 2 sin 2 1 x 2 5 0 2 } d d x } sin 2 1 ( x ) 5 2 25. } d d x } cot 2 1 x 5 } d d x } 1 } p 2 } 2 tan 2 1 ( x ) 2 5 0 2 } d d x } tan 2 1 ( x ) 5 2 } 1 1 1 x 2 } 26. } d d x } csc 2 1 ( x ) 5 } d d x } 1 } p 2 } 2 sec 2 1 ( x ) 2 5 0 2 } d d x } sec 2 1 ( x ) 5 2 27. (a) y 5 } p 2 } (b) y 5 2 } p 2 } (c) None, since } d d x } tan 2 1 x 5 } 1 1 1 x 2 } 0. 28. (a) y 5 0 (b) y 5 p (c) None, since } d d x } cot 2 1 x 5 2 } 1 1 1 x 2 } 0. 29. (a) y 5 } p 2 } (b) y 5 } p 2 } (c) None, since } d d x } sec 2 1 x 5 0. 30. (a) y 5 0 (b) y 5 0 (c) None, since } d d x } csc 2 1 x 5 2 0. 31. (a) None, since sin 2 1 x is undefined for x . 1. (b) None, since sin 2 1 x is undefined for x , 2 1. (c) None, since } d d x } sin 2 1 x 5 } ˇ 1 w 1 2 w x w 2 w } 0. 32. (a) None, since cos 2 1 x is undefined for x . 1. (b) None, since cos 2 1 x is undefined for x , 2 1. (c) None, since } d d x } cos 2 1 x 5 2 } ˇ 1 w 1 2 w x w 2 w } 0. 33. (a) a 5 cos 2 1 x , b 5 sin 2 1 x So cos 2 1 x 1 sin 2 1 x 5 a 1 b 5 } p 2 } . (b) a 5 tan 2 1 x , b 5 cot 2 1 x So tan 2 1 x 1 cot 2 1 x 5 a 1 b 5 } p 2 } . (c) a 5 sec 2 1 x , b 5 csc 2 1 x So sec 2 1 x 1 csc 2 1 x 5 a 1 b 5 } p 2 } . 34. The “straight angle” with the arrows in it is the sum of the
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