Connecting Infinite Limits and Vertical Asymptotes

Watch it explained

How it worksHow does the sign of the denominator on each side decide which way the curve flies?
Worked exampleFind the vertical asymptotes of (x + 1)/(x² - 4) and the behavior on each side of each one.
Common mistakeWhy doesn't a zero in the denominator always create a vertical asymptote?
Ties togetherHow does a shared zero in the numerator and denominator distinguish a removable discontinuity from a vertical asymptote?

Check yourself

Your turn1 of 2

Let f(x) = (x - 13)/[(x - 5)(x - 13)], with 5 not equal to 13. The denominator is zero at two x-values, but only one of them is a vertical asymptote. Find that x-value.

End of topic.

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