Pre-Calc Homework Solutions 75

Pre-Calc Homework Solutions 75 - Section 3.2 4 Left-hand...

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4. Left-hand derivative: lim h 0 2 } f (1 1 h h ) 2 f (1) } 5 lim h 0 2 } (1 1 h h ) 2 1 } 5 lim h 0 2 1 5 1 Right-hand derivative: lim h →0 1 } f (1 1 h h ) 2 f (1) } 5 lim h →0 1 5 lim h →0 1 } 1 h 2 (1 (1 1 1 h ) h ) } 5 lim h →0 1 } h (1 2 1 h h ) } 5 lim h →0 1 2 } 1 1 1 h } 5 2 1 Since 1 2 1, the function is not differentiable at the point P . 5. (a) All points in [ 2 3, 2] (b) None (c) None 6. (a) All points in [ 2 2, 3] (b) None (c) None 7. (a) All points in [ 2 3, 3] except x 5 0 (b) None (c) x 5 0 8. (a) All points in [ 2 2, 3] except x 5 2 1, 0, 2 (b) x 5 2 1 (c) x 5 0, x 5 2 9. (a) All points in [ 2 1, 2] except x 5 0 (b) x 5 0 (c) None 10. (a) All points in [ 2 3, 3] except x 5 2 2, 2 (b) x 5 2 2, x 5 2 (c) None 11. Since lim x 0 tan 2 1 x 5 tan 2 1 0 5 0 y (0), the problem is a discontinuity. 12. lim h 0 2 } y (0 1 h h ) 2 y (0) } 5 lim h 0 2 } h h 4/5 } 5 lim h 0 2 } h 1 1/5 } 5 2‘ lim h 0 1 } y (0 1 h h ) 2 y (0) } 5 lim h 0 1 } h h 4/5 } 5 lim h 0 1 } h 1 1/5 } 5 ‘ The problem is a cusp. 13. Note that y 5 x 1 ˇ x 2 w 1 2 5 x 1 ) x ) 1 2 5 5 lim h 0 2 } y (0 1 h h ) 2 y (0) } 5 lim h 0 2 } 2 2 h 2 } 5 lim h 0 2 0 5 0 lim h
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