Pre-Calc Homework Solutions 73

Pre-Calc Homework - Section 3.1 22 We show that the right-hand derivative at 1 does not exist lim h0 73(e Yes the one-sided limits exist and are

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22. We show that the right-hand derivative at 1 does not exist. lim h 0 1 } f (1 1 h h ) 2 f (1) }5 lim h 0 1 } 3(1 1 h h ) 2 (1) 3 } 5 lim h 0 1 } 2 1 h 3 h } 5 lim h 0 1 1 } 2 h } 1 3 2 5‘ 23. lim h 0 1 } f (0 1 h h ) 2 f (0) }5 lim h 0 1 } ˇ h w 2 h ˇ 0 w }5 lim h 0 1 } ˇ h h w } 5 lim h 0 1 } ˇ 1 h w }5‘ Thus, the right-hand derivative at 0 does not exist. 24. Two parabolas are parallel if they have the same derivative at every value of x . This means that their tangent lines are parallel at each value of x . Two such parabolas are given by y 5 x 2 and y 5 x 2 1 4. They are graphed below. [ 2 4, 4] by [ 2 5, 20] The parabolas are “everywhere equidistant,” as long as the distance between them is always measured along a vertical line. 25. For x .2 1, the graph of y 5 f ( x ) must lie on a line of slope 2 2 that passes through (0, 2 1): y 52 2 x 2 1. Then y ( 2 1) 52 2( 2 1) 2 1 5 1, so for x ,2 1, the graph of y 5 f ( x ) must lie on a line of slope 1 that passes through
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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