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

$$$$$$Findtheverticalasymptots$$$$$$$$of,f\left(x\right)=\tan \left(\frac{\pi }{2x+2}\right)in$$$$$$$$[0,4]$$$$-------------$$$$$$

Answered by efronzo1 last updated on 18/Nov/24

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

Commented by mnjuly1970 last updated on 18/Nov/24

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