Unit 1 Assessment Project
1. Create a formula for the distance of an object at any time t. The formula must be at least degree 2 with a minimum of 2 terms. Using your formula you must:
· Determine average velocity of the object for the first 10 seconds.
· Determine, with an explanation, the instantaneous velocity after 10 seconds.
· Determine, with an explanation, the instantaneous velocity for any time t.
· Determine if the object is ever traveling 50 m/s.
2. Create a piecewise function over the domain of the real numbers. The function must contain at least 3 different pieces and may not be continuous and may not have a limit at at least one point. Using your function you must:
· Provide a graph of your function.
· Explain why your function is not continuous at the specific point.
· Explain why a limit does not exist at the point above. Explain how you could change your function such that there is a limit. Calculate the left and right side limits at this point.
3. Demonstrate, through a real life application, how you can calculate the instantaneous rate of change at a specific data point. You may use data from a chart, create a video, etc., but the data may not follow a specific function. The point at which you calculate the rate is entirely up to you, but must have an explanation.
4. Create three functions, one which:
· approaches infinite,
· one which approaches 0,
· and another which approaches a line which is not 0
as you extend these functions to infinite. Explain how you can determine the limit as x approaches infinite, for each of your functions.
5. Create a real life example of a convergent series, and calculate the sum of this series.