Definitions
If the left and right hand limits are not the same, then we say that the limit.....
What is DNE or Does Not Exist
This is the limit as x approaches infinity of (2x^2-7x+4)/(2-5x - 4x^2)
What is -1/2
This is the limit as x approaches -2 of the function
(x^2 - 4)/(x + 2)
What is -4
This is the limit as x approaches 3 of the function
f(x) = (x^3 + 1)/(x-1)
What is 14
This is the limit as x approaches 2 of (x^2-2x)/(x^2-x-2)
What is 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.
What is a 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.
What is a VERTICAL ASYMPTOTE
This is the limit as x approaches -1 of the function
1/(x+1)
What is - infinity
These are all the x values with REMOVABLE discontinuities.
What is x=4 and 6.
This is the limit as x approaches 0 of
(x^2-8x)/x
What is -8
If the limit at a certain value equals the actual value of the function, we say that the function is _______________ at that value
What is continuous
This is the limit as x approaches infinity of (5x^3-7x+1)/(7x-1).
What is DNE or positive infinity
This is the type of discontinuity at x=4 for the piecewise function
f(x) = 2x+3, x<4
f(x) = 4x-2, x>=4
What is JUMP DISCONTINUITY.
This is limit as x approaches 3
f(x) = 1/(x -3)
What is DNE.
This is the limit as x approaches 0 of ((4+x)^2-16)/x
What is 8.
Name the different types of discontinuities
What is a hole, jump or vertical asymptote
This is the limit as x approaches infinity of (x^2+x)/(3-x)
What is NEGATIVE INFINITY
Given f(x) = 2x^3 - 8x +1, what is f(2)
What is 1
This is the limit as x approaches 4-
f(x) = 4x^2/(x^2 - 4x)
What is -infinity
This is the limit as x approaches 0
f(x) = 4sin3x/5x
What is 12/5
This is the special name for a function that has different rules for different intervals of x
What is a PIECEWISE function
This is the limit as x approaches infinity of any function that looks like 1/x^n
What is 0.
Name the type of discontinuity, if any, using the definition of continuity
f(x) = 4x + 7, x not equal to 1
f(x) = 11, x=1
Function is continuous everywhere
The value of a, if the function is continuous at x=1
f(x) = 2a + 3x, x not equal to 1
f(x) = 6x, x = 1
What is a=3/2
This is the limit as x approaches -4 of ((1/4)+(1/x))/(4+x).
What is -1/16.