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Question Number 92511 by Ar Brandon last updated on 07/May/20

$$\underset{\mathrm{x}\to 0}{\lim }\frac{\sqrt[3]{\mathrm{x}}-\sqrt[5]{\mathrm{x}}}{\sqrt[3]{\mathrm{x}}-\sqrt[4]{\mathrm{x}}}$$

Commented by john santu last updated on 07/May/20

$$\mathrm{x}={\mathrm{t}}^{60}$$$$\underset{\mathrm{t}\to 0}{\lim }\frac{{\mathrm{t}}^{20}-{\mathrm{t}}^{12}}{{\mathrm{t}}^{20}-{\mathrm{t}}^{15}}=\underset{\mathrm{t}\to 0}{\lim }\frac{{\mathrm{t}}^{12}({\mathrm{t}}^8-1)}{{\mathrm{t}}^{15}({\mathrm{t}}^5-1)}$$$$=\underset{\mathrm{t}\to 0}{\lim }\frac{{\mathrm{t}}^8-1}{{\mathrm{t}}^3({\mathrm{t}}^5-1)}=\mathrm{DNE}$$

Commented by Ar Brandon last updated on 07/May/20

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