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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