Find-the-vertical-asymptots-of-f-x-tan-pi-2x-2-in-0-4-

Question Number 213841 by mnjuly1970 last updated on 18/Nov/24

$$ \\ $$$$\:\:{Find}\:{the}\:{vertical}\:{asymptots} \\ $$$$\: \\ $$$$\:\:{of}\:\:,\:\:\:{f}\left({x}\right)=\:\mathrm{tan}\left(\frac{\:\pi}{\mathrm{2}{x}\:+\:\mathrm{2}}\:\right)\:\:{in}\: \\ $$$$\: \\ $$$$\:\:\:\:\:\left[\:\mathrm{0}\:\:,\:\:\:\mathrm{4}\:\right] \\ $$$$\:−−−−−−−−−−−−− \\ $$$$ \\ $$

Answered by efronzo1 last updated on 18/Nov/24

$$\:\:\mathrm{Let}\:{x}=\:{c}\:\:\mathrm{be}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{asymptot}\: \\ $$$$\:\:\underset{{x}\rightarrow{c}} {\mathrm{lim}}\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{2x}+\mathrm{2}}\right)\:=\:\infty\: \\ $$$$\:\:\mathrm{it}\:\mathrm{follow}\:\mathrm{that}\:\frac{\pi}{\mathrm{2x}+\mathrm{2}}\:=\:\frac{\pi}{\mathrm{2}}\:\mathrm{or}\:\frac{\pi}{\mathrm{2x}+\mathrm{2}}\:=\:\frac{\mathrm{3}\pi}{\mathrm{2}} \\ $$$$\:\:\Rightarrow\mathrm{2x}+\mathrm{2}\:=\:\mathrm{2}\:;\:\mathrm{x}=\:\mathrm{0} \\ $$$$\:\:\Rightarrow\mathrm{2x}+\mathrm{2}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:;\:\mathrm{x}<\mathrm{0}\: \\ $$

Commented by mnjuly1970 last updated on 18/Nov/24

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