Intro to Asymptotic notation

Intro to Asymptotic notation

García Martínez Braulio Israel 3301159

Asymptote (definition and etymology)

Asymptote is a straight line that approaches a curve indefinitely but without ever finding it.

ασύμπτωτο

The word asymptote deriver from the Greek "asymtotos" formed with the privative prefix "a-", the adverb "sym" ande derivativeof the verb pipetein.

Types of asymptotes

Horizontal asymptotes

They are lines perpendicular to the axis of the ordinates, with equation y = const lim_(x→∞)⁡〖f(x)=k〗 ó lim_(x→−∞)⁡〖f(x)〗 So the line y = k is a horizontal asymptote for the graph of f(x)

lim_(x→∞)⁡〖x/(1+x^2 )〗= 0

Vertical asymptotes

They are lines perpendicular to the abscissa axis, with equation x = const lim_(x→k−)⁡〖f(x)= ±∞ or lim_(x→k+)⁡〖f(x)= ±∞〗 〗 Then the line x = k is a vertical asymptote for the graph of f(x)

lim_(X→2)⁡〖x^2/(2−x)=∞〗

Oblique asymptotes

Oblique asymptotes will only be found when there are no horizontal asymptotes. For an oblique asymptote to exist, the degree of the numerator must be exactly one degree greater than that of the denominators, so the asymptote is given by y = mx + b Where: m=lim_(x→∞)⁡〖(f(x))/x〗 and b= lim_(x→)⁡[f(x)−mx]

f(x)= (x^2+2)/(x−2)

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