Limits
Continuity
How to find a derivative
What do derivatives tell us about?
Miscellaneous
100
What is a limit?
The value that a function "approaches" as x approaches some value.
100
What is a function?
A continuous line that has only one X value for every Y value
100
What is the derivative
measures the instantaneous rate of change of a function with respect to the independent variable
100
What can derivatives tell us about change?
The rate at which variables change
100
Why did we need to learn limits first before continuity?
Because you need to be able to determine a limit in order to determine if a function is continuous.
200
What are the right and left end behaviors?
the two sides of a limit.
200
What are the types of discontinuity?
Holes, Jumps, and Asymptotes
200
What is the simplest differentiation
nx^n-1
200
What does graphing a derivative show you?
The slopes of a function
200
Where is the hole in this function: (x^2+3x-4/x+4)
(x-1)
300
What does the Limit of a function do as it approaches infinity?
It gets really really close to zero, but never reaches it.
300
How do you fill in a hole?
Factor a discontinuous function and then simplify until you have a new function.
300
What is the product rule
f1(x) * g(x)+ f(x) * g1(x)
300
How are derivatives used for efficiency?
Through finding max and minimums, jerk, acceleration, profit margins, related rates Ex.
300
Is this interval open? closed? or both? (a,b]
Both: Open and closed
400
Can a limit exist, but the point not exist?
Yes
400
What is intermediate value theorem
the theorem that states a function is continuous on a closed interval that takes on every value between function A and Function B
400
What is the quotient rule (f(x)/g(x))
f1(x) * g(x)- f(x) * g1(x) / g(x)^2
400
When finding dx/dy, what are you actual finding? Think about the relationship between the dependent variable and the independent variable.
When x is changing, how y is changing or how x is changing with the respect too how y is changing
400
What is the derivative of (sin(tan(3x^3+4)))
Cos(tan(3x^3+4))* sec^2(3x^3+4) * (9x^2)
500
How do you find vertical and horizontal asymptotes or "infinite functions"
Horizontal: determine by the highest term on numerator and denominator Vertical: Whatever makes the denominator zero
500
What are the three parameters that make a function continuos?
1. If the Left and Right end behaviors go to the same spot 2.Both X and Y exist: a point. 3. If the limit and the point are the same
500
What is chain rule ((u)^n)
n(u)^n-1*u1
500
When looking at a graph of a third degree, what will the graph of the derivative look like? How about the second derivative?
Like a second degree graph-parabola Like a first degree graph- straight line
500
A limit can only exist if....
the left and right hand meet at the same point.
M
e
n
u