In Activity 1.1.1βs Figure 1 we found an approximation to the limit of the function as tends to 2. Now let us say you are also given a table of numerical values (Table 8) for the function. Given this new information which of the choices below best describes the limit of the function as tends to 2?
There is not enough information because we do not know the value of the function at .
The limit can be approximated to be 1 because the data in the table and the graph show that from the left and the right the function approaches 1 as goes to 2.
The limit can be approximated to be 1 because the values appear to approach 1 and the graph appears to approach 1, but we should zoom in on the graph to be sure.
The limit cannot be approximated because the function might not exist at .
Answer.
C. The limit can be approximated to be 1 because the values appear to approach 1 and the graph appears to approach 1, but we should zoom in on the graph to be sure.
In this activity you will study the velocity of Usain Bolt in his Beijing 100 meters dash. He completed 100 meters in 9.69 seconds for an overall average speed of 100/9.69 = 10.32 meters per second (about 23 miles per hour). But this is the average velocity on the whole interval. How fast was he at different instances? What was his maximum velocity? Letβs explore this. The table Table 12 shows his split times recorded every 10 meters.
What is your best estimate for the Usainβs velocity at the instant when he passed the 50 meters mark? This is your estimate for the instantaneous velocity.
Using the table of values, explain why 50 meters is NOT the best guess for when the instantaneous velocity was the largest. What other point would be more reasonable?