Definitions
If the left and right hand limits disagree, then we say that the limit.....
DNE or Does Not Exist
What is the limit as x approaches infinity of (2x^2-7x+4)/(4x^2-5x+2)
1/2
What is the limit of x/x as x approaches 0?
1
Find the horizontal asymptote(s) of the following function: y=(8x²+3x+4)/(2x²+99).
Both polynomials are to the second degree, so the asymptote is at y=8/2 or y=4.
What is the limit as x approaches 2 of (x^2-2x)/(x^2-x-2)
2/3
If the limit approaching either positive or negative infinity equals a certain value, then we can conclude that there is a ________________________ at that value.
HORIZONTAL ASYMPTOTE
If the limit as x approaches a certain value is equal to positive or negative infinity, then we can conclude that there is a __________________ at that value.
VERTICAL ASYMPTOTE
What is the limit of sin x/(x^2+3x) as x approaches 0?
1/3
Is f(x)=x^2 x is not =2, and 1 x=2, continuous at x=2?
No this is a removable discontinuity at x=2.
What is the limit as x approaches 9 of (x^2-81)/(sqrt(x) -3).
108.
If the limit at a certain value equals the actual value of the function, we say that the function is _______________ at that value
continuous
What is the limit as x approaches infinity of (4x^2-7x+1)/(2x-1).
positive infinity
Where is the function f(x)=(x^2-4)/(x-2) discontinuous?
x=2
Determine if the following function is continuous at x=-2. f(x)= {x²+2x if x≤-2, x^3-6x if x≥-2.
The left hand limit is 0 and the right hand limit is 4. Since the left and right hand limits are not equal, a limit does not exist at x=-2.
What is the limit as x approaches 0 of ((4+h)^2-16)/h
8.
This type of discontinuity occurs when the graph is blocked by an asymptote
INFINITE DISCONTINUITY
What is the limit as x approaches infinity of (x^2+x)/(3-x)
NEGATIVE INFINITY
Is f(x)=(x^2+2) x<1, and (4) x>1 continuous at x=1?
No it is not continuous at x=1 because as x approaches 1 from the left the limit is 3 and from the right the limit is 4.
For what x values is the function (x²+2x-8)/(x²+3x-4) continuous?
The function is continuous on all values except x=-4.
hole
This is the special name for a function that is broken up at a particular value of x. f(x) = { 2x+3, x<2, 4x-1, x>2}
PIECEWISE function
What is the limit as x approaches infinity of any function that looks like 1/x^n
0
Describe the limits as x approaches ∞ and -∞. f(x)= x^3-4x^2+7.
Limit as x approaches ∞ is ∞. Limit as x approaches -∞ is -∞.
What vertical and horizontal asymptotes (if any) does the graph of y=(x^2-9)/(3x-9) have?
There are no horizontal or vertical asymptotes, but the function is has a removable discontinuity at x=3.
-a/b