What are the vertical asymptotes of #f(x) = (2)/(x^2 - 1)#?

Answer 1

Vertical asymptotes for this function will occur when the denominator is negative. Therefore, it behooves us to find the zeroes of the function in the denominator, namely #x^2 -1#. Factoring, we get #x^2-1 = (x-1)(x+1)# and thus our zeroes occur at #x=+-1#. Ergo, the locations of our vertical asymptotes are also #x=+-1#.

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Answer 2

Liam Brennan

The vertical asymptotes of ( f(x) = \frac{2}{x^2 - 1} ) occur where the denominator equals zero. So, to find the vertical asymptotes, you set the denominator equal to zero and solve for ( x ).

( x^2 - 1 = 0 )

This equation can be factored as ( (x - 1)(x + 1) = 0 ).

Therefore, the vertical asymptotes occur at ( x = 1 ) and ( x = -1 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.