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Arithmetic Progression

Let f x = x...

Question

Let $f (x) = x^{5} [\frac{1}{x^{3}}], x \neq 0$ and $f (0) = 0,$ then find $lim x \to 0 f (x) .$

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Solution

$f (x) = x^{5} [\frac{1}{x^{3}}]$

$= x^{2}$

${lim}_{x \to 0} f (x)$

$= {lim}_{x \to 0} (x^{2})$

$= 0$

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