Calculus

True or false.

1. If f(x) has a vertical asymptote at x=a, then the limit of f(x) as x --> a from the left is negative infinite and the limit of f(x) as x--> a from the right is positive infinite.

I think this is true. Take for instance, a rational function. the two curves each has a limit going in the opposite direction. Thus, the limit does not exist and hence there is a vertical asymptote.

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  1. BZZT! But thanks for playing.

    Consider f(x) = 1/(x-a)^2

    The limit from both sides is +∞

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