# From Sequence to Function

Calculus Level 4

It is a well known fact that if $$\sum a_i$$ converges, then $$\lim a_i = 0$$.

True or false:

If $$f$$ is a continuous function such that $$\int_0^\infty f(x) \, dx$$ exists and is finite, then $\lim_{x \rightarrow \infty } f(x) = 0 .$

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