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`lim_(x->0){tan(pi/4+x)}^(1/x)`

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`lim_(x->0){tan(pi/4+x)}^(1/x)`
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1 Answer

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Best answer
`lim_(x->0)((tan(pi/4)+tanx)/(1-tan(pi/4)tanx))^(1/x)`
`lim_(x->0)((1+tanx)/(1-tanx))^(1/x)`
`lim_(x->0)(1+(2tanx)/(1-tanx))^(1/x)`
`lim_(x->0)(2tanx)/x*(1/(1-tanx))`
`e^(2*1*(1/(1-0))`
`e^2`.
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