Limits
Continuity
Misc. + Definitions
Limits and Asymptotes
Limits Involving Infinity
100
Determine lim {as x-> 0} 1/x .
What is DNE
100

Name a function that is always continuous

What is polynomials?

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 this function continuous at x=-3? f(x)= (x²-9)/(x+3). Explain why.

What is yes?

200

Emma's dog's name

What is Jack

200

Find the vertical asymptotes of Determine the horizontal asymptote of f(x)= (x-1)/(x²-2x+1).

What is x = 2?

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 discontinuity in the function f(x)= (x+1)/(4-x²) .

What is x=-2 and x=2

300

What must be true for a limit to exist?

What is the limit from the left must equal the limit from the right?

300

Explain how to find a vertical asymptote

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

How do you answer discontinuity questions on a test?

What is by explaining which of the three conditions the function breaks?
400

Explain how to find a horizontal asymptote

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). Or BOBO, BETC, BOTS

400

Give an example of a BOBO function

What is 1/x

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

Emma's astrological sign

What is Leo?

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

Give an example of a BETC function

3x/4x

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