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Question Number 145549 by physicstutes last updated on 05/Jul/21

$$\mathrm{Find}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{asymptotes}\mathrm{to}\mathrm{the}\mathrm{curve}$$$$y=f\left(x\right)\mathrm{where}f\left(x\right)=\ln \left(\frac{x+3}{x-1}\right).$$

Answered by gsk2684 last updated on 06/Jul/21

$$\mathrm{function}\mathrm{is}\mathrm{defined}\mathrm{only}\mathrm{if}$$$$0<\frac{\mathrm{x}+3}{\mathrm{x}-1}\Rightarrow 0<(\mathrm{x}+3)(\mathrm{x}-1)$$$$\mathrm{x}<(-3)\mathrm{or}1<\mathrm{x}$$$$\mathrm{function}\mathrm{has}\mathrm{asymptotes}\mathrm{at}$$$$\mathrm{x}=-3,1\mathrm{also}\mathrm{function}\mathrm{never}\mathrm{be}0.$$$$\mathrm{x}\mathrm{axis}\mathrm{is}\mathrm{also}\mathrm{an}\mathrm{asymptote}.$$

Commented by gsk2684 last updated on 06/Jul/21

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