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Pre-Calc Homework Solutions 76

# Pre-Calc Homework Solutions 76 - 76 Section 3.2 27 3(4 x3...

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21. continued Check x 5 3: Since g (3) 5 (4 2 3) 2 5 1 and lim x 3 2 g ( x ) 5 lim x 3 2 (2 x 1 1) 5 2(3) 1 1 5 7, the function is not continuous (and hence not differentiable) at x 5 3. The function is differentiable for all reals except x 5 3. 22. Note that C ( x ) 5 x ) x ) 5 5 , so it is differentiable for all x except possibly at x 5 0. Check x 5 0: lim h 0 } C (0 1 h h ) 2 C (0) } 5 lim h 0 } h ) h ) h 2 0 } 5 lim h 0 ) h ) 5 0 The function is differentiable for all reals. 23. (a) x 5 0 is not in their domains, or, they are both discontinuous at x 5 0. (b) For } 1 x } : NDER 1 } 1 x } , 0 2 5 1,000,000 For } x 1 2 } : NDER 1 } x 1 2 } , 0 2 5 0 (c) It returns an incorrect response because even though these functions are not defined at x 5 0, they are defined at x 5 6 0.001. The responses differ from each other because } x 1 2 } is even (which automatically makes NDER 1 } x 1 2 } , 0 2 5 0) and } 1 x } is odd. 24. [ 2 5, 5] by [ 2 10, 10] } d d y x } 5 x 3 25. [ 2 2 p , 2 p ] by [ 2 1.5, 1.5] } d d y x } 5 sin x 26. [ 2 6, 6] by [ 2 4, 4] } d d y x } 5 abs ( x ) or ) x ) 27.
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