Limits
The lim {as x-> 0} 1/x .
What is DNE?
The points of discontinuity for the function y= 1/(x+2)² . Identify the type of discontinuity.
What is x= -2; infinite discontinuity?
The value that a function or expression approaches as the domain variable(s) approach a specific value.
What is the limit?
Determine the horizontal asymptote of f(x)= (2x-1)/(x²-2x+1).
What is y=0?
Determine lim {as x approaches infinity} (3x + 1)/( |x| + 2).
What is 3?
The lim {as x -> 1} (x³ + 3x² - 2x -17)
What is -15?
The continuity of the function f(x)= (x²-9)/(x+3) at x=-3.
What is discontinuous?
A function with a connected graph.
What is a continuous function?
The vertical asymptotes of f(x)= 1/x² .
What is x=0?
Determine the lim {as x approaches infinity} (x³+5x)/(2x³-x²+4) .
What is 1/2?
The lim {as x ->(-½)} 3x²(2x - 1)
What is -3/2?
The points of disconinuity in the function f(x)= (x+1)/(4-x²) .
What is x=-2 and x=2?
A function with a graph that is not connected.
What is a discontinuous function?
How to find a vertical asymptote analytically of a rational function. *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?
Determine lim {as x approaches infinity} [5x+sin(x)] / x .
What is 5?
The lim {as x-> 0+} x/|x|.
What is 1?
The three factors that determine continuity.
What is f(c) exists, the lim {as x-> c} exists, and f(c)= lim {as x ->c}?
Can be classified as either removable or essential. There are several kinds of essential discontinuities, one of which is the jump ...
What is Discontinuity?
Finding the horizontal asymptote analytically of a rational function. *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).
Determine lim {x->0-} 3/x
What is (negative infinity)?
The lim {as x -> 1} (x-1)/(x²-1).
What is 1/2?
The points of discontinuity of the function 1/(x²+1) .
What is none?
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?
An ______ is a value that you get closer and closer to, but never quite reach. *provide examples*
What is Asymptote Horizontal or Vertical Asymptote?
Determine lim {x->-3+} -2/(x+3)^3
What is (positive infinity)?