Computing an instantaneous velocity from average velocities, + the ans trick | Calculus (limits)

The instantaneous velocity can (and must!) be inferred from average velocities as the duration of time goes to 0. In this video, Prof. Amethyst demonstrates how to find an instantaneous velocity. Along the way, she shows how to compute average velocities, and techniques for computing them quickly on a TI calculator using "the ans trick". This trick can save so much time if you have to repeatedly evaluate an expression in your calculator, and just one value is changing.

This video has ADA-compliant captions.

0:00 Intro
0:38 Problem overview
2:20 Estimate instantaneous via average using a table
3:04 Average rate of change for delta t=0.1, [.8, .9]
4:24 The ans trick – t is ans
7:18 Average rate of change for delta t=0.01, [.8, .81]
8:51 Average rate of change for delta t=0.001, [.8, .801]
9:10 Ans trick, Δt is ans
10:38 Observe the power of the ans trick, Average rate of change for delta t=0.0001, [.8, .8001]
12:40 From average to instantaneous rate of change
13:51 Conclusion

Computinginstantaneousvelocity