Calc02_1day1 - 2.1 Rates of Change and Limits Grand Teton...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
2.1 Rates of Change and Limits Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007 Grand Teton National Park, Wyoming
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Suppose you drive 200 miles, and it takes you 4 hours. Then your average speed is: mi 200 mi 4 hr 50 hr ÷ = distance average speed elapsed time x t = = If you look at your speedometer during this trip, it might read 65 mph. This is your instantaneous speed .
Background image of page 2
A rock falls from a high cliff. The position of the rock is given by: 2 16 y t = After 2 seconds: 2 16 2 64 y = = average speed: av 64 ft ft 32 2 sec sec V = = What is the instantaneous speed at 2 seconds?
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
instantaneous y V t for some very small change in t ( 29 ( 29 2 2 16 2 16 2 h h + - = where h = some very small change in t We can use the TI-89 to evaluate this expression for smaller and smaller values of h .
Background image of page 4
instantaneous y V t ( 29 ( 29 2 2 16 2 16 2 h h + - = h y t 1 80 0.1 65.6 .01 64.16 .001 64.016 .0001 64.0016 .00001 64.0002 ( 29 ( 29 { } 16 2 ^ 2 64 1,.1,.01,.001,.0001,.00001 h h h + - ÷ = We can see that the velocity approaches 64 ft/sec as h becomes very small.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/14/2009 for the course CALC 071265836 taught by Professor Sorray during the Spring '09 term at Air Force Institute of Technology, Ohio.

Page1 / 19

Calc02_1day1 - 2.1 Rates of Change and Limits Grand Teton...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online