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
