Unit One: Limits Flashcards
How do you find the limit of a tangent line?
Pre-calc
Chose a really close x, find out y, and figure slope from that
How do you find the limit of the area of a curve? (Pre-calc)
Use as many rectangles as possible
Do limits matter at a point?
No, but both sides have to go to the same place
What happens when you plug in a number trying to get a limit and you get 0/0?
There is a limit, but you have to change the equation
What happens when you plug in a number trying to get a limit and you get #/0?
There is a VA at that point
What is the limit as k->0 of (sink)/k
1
What is the limit as k->0 of (1-cosk)/k
0
What are the three requirements of a continuous function at a number (ex:c)?
F(c) is defined, the limit as x->c exists, and they are equal
When is a discontinuity removable/non-removable?
If a limit exists, it is removable
How do you write a limit from the left or right?
Left- Limit as x-c^- Right- Limit as x-c^+
Does a step function have an open or closed circle at zero?
Closed
When is a function continuous on a closed interval {a,b}?
When it is continuous on the open interval (a,b) and the limit as x goes to a from the right exists, and the limit as x goes to b from the left exists
What is the Intermediate Value Theorem?
If f is continuous on {a,b} and k is any number between f(a) and f(b), then there exists at least one # c such that f(c)=k
What is the HA if the degree of the numerator is less than the degree of the denominator?
0
What is the HA if the degree of the numerator is greater than the degree of the denominator?
DNE
What is the HA if the degree of the numerator is equal to the degree of the denominator?
ratio of leading coefficients
What kind of symmetry exists if f(-x)=f(x)?
Y-axis
What kind of symmetry exists if f(-x)=-f(x)?
Origin
