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Question Number 192846 by mathlove last updated on 29/May/23

$$\underset{h\to 0}{\lim }\frac{3h}{\sqrt[5]{3h+x}-\sqrt[5]{x}}=?$$

Answered by MM42 last updated on 29/May/23

$$forf\left(x\right)=\sqrt[5]{x}\Rightarrow f^{\prime }\left(x\right)=\frac{1}{5\sqrt[5]{x^4}}$$$${lim}_{h\to 0}\frac{3h}{\sqrt[5]{3h+x}-\sqrt[5]{x}}=\frac{1}{f^{\prime }\left(x\right)}=5\sqrt[5]{x^4}$$

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