Is it Cauchy?

Calculus Level 1

Consider the metric space consisting of continuous functions on [0,1][0,1] with the metric d(f,g)=01f(x)g(x)dx.d(f,g)=\int_0^1 |f(x)-g(x)|\, dx. Is the sequence fn(x)=xnf_n(x)=\frac xn a Cauchy sequence in this space?

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