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Precalc0110to0111-page20

Precalc0110to0111-page20 - ± 0.1 = 2.71 mph 0.99 1 ± ²...

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(Section 1.11: Limits and Derivatives in Calculus) 1.11.9 We could also consider this approach: Interval Value of h Average velocity, s 1 + h () ± s 1 () h (rounded off to six significant digits) 1, 2 ± ² ³ ´ 1 hour 7.00000 mph 1, 1 1 60 ± ² ³ ´ µ 1 minute 3.05028 mph 1, 1 1 3600 ± ² ³ ´ µ 1 second 3.00083 mph ± 0 + ± 3 mph Here, we let h ± 0 ² . Interval Value of h (in hours) Average velocity, s 1 + h () ± s 1 () h 0, 1 ± ² ³ ´ ± 1 s 0 () ± s 1 () ± 1 = 1 mph 0.9, 1 ± ² ³ ´ ± 0.1 s 0.9 () ± s 1
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Unformatted text preview: ( ) ± 0.1 = 2.71 mph 0.99, 1 ± ² ³ ´ ± 0.01 s 0.99 ( ) ± s 1 ( ) ± 0.01 = 2.9701 mph 0.999, 1 ± ² ³ ´ ± 0.001 s 0.999 ( ) ± s 1 ( ) ± 0.001 = 2.997001 mph ± ² ± 3 mph • Because of the way we normally look at slopes, we may prefer to rewrite the difference quotient s ( ) ± s 1 ( ) ± 1 as s 1 ( ) ± s ( ) 1 , and so forth. (See Footnote 2.) §...
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