Question

For function f(x), which pair of limits would verify the existence of a vertical asymptote at x = –1?

Answer 1

This shows that for the function f(x), the pair of limits that would verify the existence of a vertical asymptote at x = –1 is expressed as:

$\lim_{x \to -1^+} a_n = \lim_{x \to -1^-} a_n =f(c)$

Limit of a function

For the limit of a function to be continuous at a point x = a, the left hand limit of the function must be equal to the right hand limit.

Mathematically, the expression below must be true

$\lim_{x \to a^+} a_n = \lim_{x \to a^-} a_n =f(c)$

This shows that for the function f(x), the pair of limits that would verify the existence of a vertical asymptote at x = –1 is expressed as:

$\lim_{x \to -1^+} a_n = \lim_{x \to -1^-} a_n =f(c)$

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