Limits
Continuity
Definitions
Limits and Asymptotes
Limits Involving Infinity
100
Determine lim {as x-> 0} 1/x .
What is DNE
100
Find the points of discontinuity for the function y= 1/(x+2)² . Identify the type of discontinuity.
What is x= -2; infinite discontinuity
100

The value that a function or expression approaches as the domain variable(s) approach a specific value. 

What is Limit

100
Determine the horizontal asymptote of f(x)= (2x-1)/(x²-2x+1).
What is y=0 (the x-axis)
100
Determine lim {as x approaches infinity} (3x + 1)/( |x| + 2).
What is 3
200
Determine lim {as x -> 1} (x³ + 3x² - 2x -17)
What is -15
200
Is continuous at x=-3 for the function f(x)= (x²-9)/(x+3) .
What is y=x-3
200
A function with a connected graph.
What is a continuous function
200
Find the vertical asymptotes of f(x)= 1/x² .
What is x=0
200
Determine the lim {as x approaches infinity} (x³+5x)/(2x³-x²+4) .
What is 1/2
300
Determine lim {as x ->(-½)} 3x²(2x - 1)
What is -3/2
300
Find all points of disconinuity in the function f(x)= (x+1)/(4-x²) .
What is x=-2 and x=2
300
A function with a graph that is not connected.
What is a discontinuous function?
300
How to find a vertical asymptote analytically. *provide an example to get points*
What is Factoring the numerator and denominator of a rational function and simplifying the fraction can provide information about the function near a possible asymptote.
300
Determine lim {as x approaches infinity} [5x+sin(x)] / x .
What is 5?
400
Determine lim {as x-> 0+} x/|x|
What is 1
400
The three factors that determine continuity
What is f(c) exists, the lim {as x-> c} exists, and f(c)= lim {as x ->c}
400

Can be classified as either removable or non-removable. There are several kinds, one of which is the jump ...

What is Discontinuity?

400
Find the horizontal asymptote analytically. *provide an example to get points*
What is If both polynomials are the same degree, divide the coefficients of the highest degree terms. If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0).
400
f(x) = 3/x
What is (negative infinity).
500
Determine lim {as x -> 1} (x-1)/(x²-1).
What is 1/2
500
Find the points of discontinuity of the function 1/(x²+1) .
What is none
500

f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the ________ .

What is End behavior.

500
An ______ is a value that you get closer and closer to, but never quite reach. *provide examples*
What is Asymptote Horizontal or Vertical Asymptote.
500
h(x)=-2/x^3
What is (positive infinity)
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