| Limits |
| #1 |
What's the idea that you can get close to something without actually reach it? |
A Limit |
| #2 |
What are the 3 types of limits? |
A limit from the left, a limit from the right, and the total or combined limit. |
| #3 |
When does a total limit exist? |
When the limit from the left is equal to the limit from the right. |
| #4 |
What are two methods of finding a limit? |
Direct Substitution and Algebraic Manipulation |
| #5 |
What is the The Limit, as delta x approaches 0, of f of x plus delta x minus f of x divided by delta x. |
The derivative |
| Rates |
| #1 |
If you borrow $100 at 10% interest, you pay back $110 after 1 year. What is the rate and the units of the rate? |
the rate is 10 ( % per year) |
| #2 |
If the price marked on the note book is 79 cents, and you by 10 for $7.90. What is the rate and the units of the rate? |
the rate is 79 (cents per notebook) |
| #3 |
If the pool is full at 10,000 gallons now, and then 2 hours later it has only 6,000 gallons. Describe what is occurring at what rate? (include units)? |
the pool is leaking at a rate of 2000 gallons per hour |
| #4 |
A position function, f(x) = x squared. f(x) is measured in meters. x is measured in seconds. What does the rate represent and what are the units |
The rate is velocity in meters per second. |
| #5 |
What is the rate of change of the velocity with respect to time including units? |
Acceleration measured in distance per time squared |
| Units, Units, Units |
| #1 |
What is meters times meters? |
meters squared |
| #2 |
What is meters divided by seconds? |
meters per second |
| #3 |
What is acceleration in meters per second squared times time in seconds (include units in answer?? |
velocity in meters per second |
| #4 |
What are the units of f ' (x), the derivative with respect to time, when f(x) is measured in meters squared? |
meters squared per second. |
| #5 |
What is volume (distance cubed) divided by distance yield? |
Surface area ( distance squared) |
| Assorted questions (Potpourri) |
| #1 |
What do you call a graph that you can completely draw without lifting your pencil from the paper? |
Continuous function |
| #2 |
What you get on a graph of f(x) when the denominator of f(x) goes to 0? |
Vertical Asymptote |
| #3 |
All the different values that x can take on of f(x). |
The domain |
| #4 |
How can you find the slope of a curved line at a point where x = a |
Find f '(a), or the slope of the tangent line that touches the curve at ( a, f(a) ) |
| #5 |
The point where the tangent line touches the curve. |
The point of tangency. |
