what is a limit?
expected y value
if there is a hole in the graph is it still a limit?
yes!
if there is a jump from one point to another…(therefore not continuous) does a limit exist?
no!
if there is a whole in the line and then a filled in circle about or below that hole which is the limit?
the hole…the intended height
when you use substitution you get three results... 1. a # 2. 0/0 3. #/0 what do they all mean?
if you get a number then that is the answer
if you get 0/0 then you need to factor reduce
if you get #/0 then they means the answer is either infinity or negative infinity
what is the limit of (sin x )/x as x approaches 0?
what about the limit of (sin 2x)/2x as x approaches 0
the limit is one for both
explain the steps to the squeeze or sandwich theorem
- separate the limit so that one has sin on its own
- put sin to be in between -1 and 1
- multiply sin, -1, and 1 by the other variable mentioned in the limit
- the values you get as a result would be shown as (a variable) is less than or equal to the original limit which is less than or equal to (another variable)..you put both of those variables in their own limit… so what is the limit of variable 1 as x approaches 0 (or whatever it says) and then find the answer and do the same for the second variable
- state what you arrive at
what is the average speed formula?
distance/time
what is the formula for instant rate of change?
the limit of (F(x+h) - F(x))/h as x approaches 0…then solve
x= the time
when finding vertical asymptotes what does it mean when
- the degree of the top is greater than the bottom
- the degree of the bottom is greater than the top
- the degrees are equal
- you have to use division to find end behavior (just do the thing where you cross out the things in the equation that dont matter then you look at the base of the equation or the end behavior and determine mentally whether it is infinity or negative infinity)
- then it is 0
- then it is the fraction of the coefficients
what is the limit of (sin x)/x as x approaches either negative infinity or infinity
zero
what is a continuous function
- draw a graph without lifting the pencil
- f is continuous on an interval if and only if it is continuous at every point on the interval
- f is continuous if its continuous at every point in its domain
what is and interior point?
a point within the intervals of a graph line or curve
what is an exterior point?
the first or last point on a graph line or curve
what are the four types of discontinuity?
- removable discontinuity
- jump discontinuity
- infinite discontinuity
- oscillating discontinuity
look at examples for types of discontinuity
now!
what is an extended function?
a function that replaces a function with a removable discontinuity
-fills in hole- so gives equation to fill in the hole
