A funny exercise from an old book

I've found the following exercise in a calculus book by Ernesto Pascal, published in 1908.

Let $latex f$ be a continuous function defined on the real line. If $latex \lim_{x \to \infty} f(x+1)-f(x)=A$, then $latex \lim_{x \to \infty} \frac{f(x)}{x}=A$.

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