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Question Number 173493 by mokys last updated on 12/Jul/22

find lim_(x→0)  tan(tanhx)−tanh(tanx)

$$\boldsymbol{{find}}\:\boldsymbol{{lim}}_{\boldsymbol{{x}}\rightarrow\mathrm{0}} \:\boldsymbol{{tan}}\left(\boldsymbol{{tanhx}}\right)−\boldsymbol{{tanh}}\left(\boldsymbol{{tanx}}\right) \\ $$

Answered by aleks041103 last updated on 12/Jul/22

just substitute  tan(tanh(0))=tan(0)=0  tanh(tan(0))=tanh(0)=0  ⇒Ans.=0−0=0  ⇒Ans.=0

$${just}\:{substitute} \\ $$$${tan}\left({tanh}\left(\mathrm{0}\right)\right)={tan}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${tanh}\left({tan}\left(\mathrm{0}\right)\right)={tanh}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\Rightarrow{Ans}.=\mathrm{0}−\mathrm{0}=\mathrm{0} \\ $$$$\Rightarrow{Ans}.=\mathrm{0} \\ $$

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