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I want to know that how can i show that the function $\displaystyle f(x)= \frac{1}{x\log x}$ continuous? Thanks in advance!

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up vote 3 down vote accepted

If $f$ and $g$ are continuous on a particular interval and $g(x) \neq 0$ for any $x$ on that interval, then $\frac{f(x)}{g(x)}$ is continuous on that interval.

$1$ is continuous on that interval. $x\log x$ is continuous and nonzero on that interval. Hence $\frac{1}{x\log x}$ is continuous.

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I think function is continuous from (1,∞).

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