# Thread: [SOLVED] limits word problem

1. ## [SOLVED] limits word problem

This problem is from a lesson on informal computation of limits:

Tom and Sue are driving along a straight, level road in a car whose speedomenter needle is broken but that has a trip odometer that can measure the distance traveled from an arbitrary point in tenths of a mile. At 2:50 pm, Tom says he would like to know how fast they are traveling at 3:00 pm, so Sue takes down the odometer readings listed in the table, makes a few calculations, and anounces the desired velocity. What is her result?

time 2:50 2:55 2:59 3:00 3:01 3:06
odometer reading 33.9 38.2 41.5 42.4 43.2 44.9

My work:

interval length 10 5 1 0 1 3 6
interval distance 8.5 4.2 0.9 x 0.8 2.5 5
average velocity 0.85 0.84 0.9 x 0.8 0.83 0.83

The velocities in the table don't seem to converge to any specific value. If the third odometer reading was 41.6 , the velocities would converge to 0.8, but I have checked and rechecked, and the book says 41.5. How do I find the velocity?

2. Originally Posted by sinewave85
This problem is from a lesson on informal computation of limits:

Tom and Sue are driving along a straight, level road in a car whose speedomenter needle is broken but that has a trip odometer that can measure the distance traveled from an arbitrary point in tenths of a mile. At 2:50 pm, Tom says he would like to know how fast they are traveling at 3:00 pm, so Sue takes down the odometer readings listed in the table, makes a few calculations, and anounces the desired velocity. What is her result?

time 2:50 2:55 2:59 3:00 3:01 3:06
odometer reading 33.9 38.2 41.5 42.4 43.2 44.9

My work:

interval length 10 5 1 0 1 3 6
interval distance 8.5 4.2 0.9 x 0.8 2.5 5
average velocity 0.85 0.84 0.9 x 0.8 0.83 0.83

The velocities in the table don't seem to converge to any specific value. If the third odometer reading was 41.6 , the velocities would converge to 0.8, but I have checked and rechecked, and the book says 41.5. How do I find the velocity?
Look at the average speed between 2:50 and 3:06, then that between 2:55 and 3:06, then between 2:59 and 3:06, then between 2:59 and 3:01.

(they wont converge, the speed at 3:00 is the maximum)

RonL