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Question Number 129072 by liberty last updated on 12/Jan/21

$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{F}\left(0\right)\mathrm{so}\mathrm{that}\mathrm{the}\mathrm{function}$$$$\mathrm{F}\left(\mathrm{x}\right)=\frac{{(4^x-1)}^3}{\sin \left(\frac{x}{4}\right)\ln (1+\frac{x^2}{3})}\mathrm{becomes}\mathrm{continous}$$$$\mathrm{at}x=0?$$

Answered by MJS_new last updated on 12/Jan/21

$${\mathrm{l}}^{\prime }\mathrm{Hopital}3\mathrm{times}\mathrm{gives}$$$$\underset{x\to 0}{\lim }F\left(x\right)=96{\left(\ln 2\right)}^3$$

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