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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

What function agrees with f at all x but -3 and 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, infinite, or 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

Determine lim {as x approaches infinity} f(x) = 3/x

What is 0.

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 limits at infinity and negative infinity.

500

An ______ is a value that you get closer and closer to, but never quite reach. 

What is Asymptote 

500

Determine lim {as x approaches negative infinity} h(x)=-2x/x^3

What is 0