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how to find vertical asymptotes

factor the denominator... value(s) of x that make denominator = 0 represent vertical asymptotes of the graph

Horizontal Asymptotes occur when

Degree of the numerator is less than the degree of the denominator

oblique asymptotes occur when...

(degree of numerator) = (degree of denominator) + 1

removable discontinuities occur when...

there is a common term in the numerator and denominator that can be canceled

the equation: y = the ratio of the leading coefficients of P(x) and Q(x)

if the degrees are equal, then the horizontal asymptote of the graph is represented by...

the equation: y = 0

if the degree of the numerator is smaller than that of the denominator, then the horizontal asymptote of the graph is represented by...

y = the quotient when P(x) is divided by Q(x)

the equation that represents the slant asymptote of the graph is the line...

the x coordinate of a hole is...

the value of x that would make the canceled term equal to zero

the y coordinate of the hole is...

the value obtained by substituting the given value of x into the reduced form of the rational function

NO!

if there is a removable discontinuity in a polynomial, does that value represent a vertical asymptote?

techniques for evaluating limits of functions

- graph the function by plugging in values

the 2 sided limit does not exist

if 2 sides of a limit approach different y values, then

the horizontal asymptote

finding the limit of f(x) as x approaches infinity is the equivalent of finding

(1.50x+4500)/x, limit A(x) = 1.50

the formula for the average cost C of a product, where x is the number of units, with each product costing 1.50 and with an up front cost of 4500 and its limit

how to simplify (n+1)!/(n-1)!; does its limit exist

(n+1)! = (n+1)+n+(n-1)!, so cancel (n-1)! to get n(n+1); no