existence of limit when both RHL and LHL approachees Positive infinity

We know that if $$lim_{x to a^+}f(x)=lim_{x to a^-}f(x)=L$$ Then $$lim_{x to a}f(x) =L$$ if $L$ is finite

But if $$lim_{x to a^+}f(x) to +infty$$ and
$$lim_{x to a^-}f(x) to +infty$$

Can we say $$lim_{x to a} f(x)$$ Does not exists since we cannot compare two infinities.

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