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lim-x-0-2-1-e-1-x-




Question Number 213128 by klipto last updated on 30/Oct/24
lim_(x→0^(+ ) ) (2/(1+e^(−(1/x)) ))
limx0+21+e1x
Answered by a.lgnaoui last updated on 30/Oct/24
lim_(x→0^(+ ) ) (2/(1+e^(−(1/x)) ))     (2/(1+e^(−(1/x)) ))=(2/(1+(1/e^(1/x) )))  =  (2/((1+e^(1/x) )/e^(1/x) ))= ((2e^(1/x) )/(1+e^(1/x) ))  donc lim _(x→o^+ ) (2/((1+e^((−1)/x) )))=2
limx0+21+e1x21+e1x=21+1e1x=21+e1xe1x=2e1x1+e1xdonclimxo+2(1+e1x)=2
Answered by MrGaster last updated on 30/Oct/24
lim_(x→0^+ ) (2/(1+e^(−(1/x)) ))=(2/(1+e^(−∞) ))=(2/(1+0))=(2/1)=2
limx0+21+e1x=21+e=21+0=21=2
Answered by Frix last updated on 31/Oct/24
(2/(1+e^(−(1/x)) ))=1+tanh (1/(2x))  lim_(x→0^+ )   (2/(1+e^(−(1/x)) )) =lim_(x→0^+ )  (1+tanh (1/(2x))) =  =1+lim_(t→+∞)  tanh t =1+1=2
21+e1x=1+tanh12xlimx0+21+e1x=limx0+(1+tanh12x)==1+limt+tanht=1+1=2

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