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Question Number 94463 by Abdulrahman last updated on 18/May/20

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{{6\mathrm{x}}^{\mathrm{k}-2}+{3\mathrm{x}}^2+10}{{3\mathrm{x}}^5+\mathrm{x}+20}$$$$\mathrm{then}{\mathrm{k}}^2+1=?$$

Commented by john santu last updated on 19/May/20

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{{6\mathrm{x}}^{\mathrm{k}-2}+{3\mathrm{x}}^2+10}{{3\mathrm{x}}^5+\mathrm{x}+20}=???$$

Commented by mathmax by abdo last updated on 19/May/20

$$={\lim }_{\mathrm{x}\to \mathrm{\infty }}2{\mathrm{x}}^{\mathrm{k}-2-5}=\lim {}_{\mathrm{x}\to \mathrm{\infty }}{2\mathrm{x}}^{\mathrm{k}-7}$$$$\mathrm{if}\mathrm{k}>7\lim =\mathrm{\infty }\mathrm{if}\mathrm{k}<7\lim =0$$$$\mathrm{if}\mathrm{k}=7\lim =2$$

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