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Hifumi's Study Notes📕Cegep 1MathematicsAsymptote

Asymptote ​

Tags
Cegep1
Mathematics
Word count
163 words
Reading time
2 minutes

Types ​

Vertical (V. A.) ​

x=a is a vertical asymptote of f(x) if any of the following is true: limx→a±f(x)=±∞

Cannot be crossed

A function can have unlimited vertical asymptotes

A limit containing an expression of the form c0 often has a vertical asymptote
The side 0 is approached from affects the direction of divergence (sign of ∞)

Horizontal (H. A.) ​

y=L is a horizontal asymptote of f(x) if limx→±∞f(x)=L

Can be crossed

A function can have at most two horizontal asymptotes

Evaluation ​

Vertical ​

For a fraction P(x)Q(x),
find all M such that Q(M)=0.
x=M is a V. A. if limx→M±P(x)Q(x)=±∞.

Horizontal ​

Find the limits limx→±∞f(x)=L.
y=L is a H. A. if L exists.

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