What's the idea that you can get close to something without actually reach it?
What are the 3 types of limits?
When does a total limit exist?
What are two methods of finding a limit?
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.
If you borrow $100 at 10% interest, you pay back $110 after 1 year. What is the rate and the units of the rate?
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?
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)?
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
What is the rate of change of the velocity with respect to time including units?
What is the derivative of y=mx+b ?
What is the derivative of f(x) = x squared ?
What is the derivative of f(x) = x cubed ?
What is the definition of the derivative in limit form?
What is the derivative of a(x) to the n power?
What is meters times meters?
What is meters divided by seconds?
What is acceleration in meters per second squared times time in seconds (include units in answer??
What are the units of f ' (x), the derivative with respect to time, when f(x) is measured in meters squared?
What is volume (distance cubed) divided by distance yield?
What do you call a graph that you can completely draw without lifting your pencil from the paper?
What you get on a graph of f(x) when the denominator of f(x) goes to 0?
All the different values that x can take on of f(x).
How can you find the slope of a curved line at a point where x = a
The point where the tangent line touches the curve.
A Limit
A limit from the left, a limit from the right, and the total or combined limit.
When the limit from the left is equal to the limit from the right.
Direct Substitution and Algebraic Manipulation
The derivative
the rate is 10 ( % per year)
the rate is 79 (cents per notebook)
the pool is leaking at a rate of 2000 gallons per hour
The rate is velocity in meters per second.
Acceleration measured in distance per time squared
m
2x
3x squared
The The Limit, as delta x approaches 0, of f of x plus delta x minus f of x divided by delta x.
(n)a(x) to the (n-1) power
meters squared
meters per second
velocity in meters per second
meters squared per second.
Surface area ( distance squared)
Continuous function
Vertical Asymptote
The domain
Find f '(a), or the slope of the tangent line that touches the curve at ( a, f(a) )
The point of tangency.
