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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. For example, the limit of as x approaches 3 is .
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 essential. There are several kinds of essential discontinuities, 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)