Pre-Calc Homework Solutions 63

Pre-Calc Homework Solutions 63 - Section 2.4 s(1 h) h s(1)...

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27. lim h 0 } s (1 1 h h ) 2 s (1) } 5 lim h 0 5 lim h 0 5 lim h 0 (3.72 1 1.86 h ) 5 3.72 The speed of the rock is 3.72 m/sec. 28. lim h 0 } s (2 1 h h ) 2 s (2) } 5 lim h 0 5 lim h 0 5 lim h 0 (45.76 1 11.44 h ) 5 45.76 The speed of the rock is 45.76 m/sec. 29. First, find the slope of the tangent at x 5 a . lim h 0 } f ( a 1 h h ) 2 f ( a ) } 5 lim h 0 5 lim h 0 5 lim h 0 } 2 ah 1 h h 2 1 4 h } 5 lim h 0 (2 a 1 h 1 4) 5 2 a 1 4 The tangent at x 5 a is horizontal when 2 a 1 4 5 0, or a 52 2. The tangent line is horizontal at ( 2 2, f ( 2 2)) 5 ( 2 2, 2 5). 30. First, find the slope of the tangent at x 5 a . lim h 0 } f ( a 1 h h ) 2 f ( a ) } 5 lim h 0 5 lim h 0 5 lim h 0 } 2 4 h 2 2 h ah 2 h 2 } 5 lim h 0 ( 2 4 2 2 a 2 h ) 52 4 2 2a The tangent at x 5 a is horizontal when 2 4 2 2 a 5 0, or a 52 2. The tangent line is horizontal at ( 2 2, f ( 2 2)) 5 ( 2 2, 7). 31. (a)
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