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f-x-x-ln-e-x-2-f-x-x-ln-e-x-2-x-ln2-f-x-x-ln-e-x-2-x-ln2-lim-x-f-x-lim-x-x-ln-e-x-2-lim-x-f-x-lim-x-x-ln-e-x-2-lim-x-

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Question Number 130455 by ayoubbacmath0 last updated on 25/Jan/21
f(x)=x+ln∣e^x −2∣ { ((f(x)=x+ln(e^x −2) x∈]ln2;+∞[)),((f(x)=x+ln(−e^x +2) x∈]−∞;ln2[)) :} lim_(x→+∞) f(x)=lim_(x→+∞) (x+ln(e^x −2))=+∞ lim_(x→−∞) f(x)=lim_(x→−∞) (x+ln(−e^x +2))=−∞ lim_(x→−∞) e^x =0 lim_(x→−∞) ln(−e^x +2)=ln2 lim_(x→−∞) (x+ln(−e^x +2)=−∞ lim_(x→^> ln2) f(x)=lim_(x→^> ln2) (x+ln(e^x −2))=−∞ lim_(x→^< ln2) f(x)=lim_(x→^< ln2) (x+ln(−e^x +2))=−∞
f(x)=x+ln∣ex−2∣{f(x)=x+ln(ex−2)x∈]ln2;+∞[f(x)=x+ln(−ex+2)x∈]−∞;ln2[limfx→+∞(x)=limx→+∞(x+ln(ex−2))=+∞limfx→−∞(x)=limx→−∞(x+ln(−ex+2))=−∞limex→−∞x=0limlnx→−∞(−ex+2)=ln2limx→−∞(x+ln(−ex+2)=−∞limfx→>ln2(x)=limx→>ln2(x+ln(ex−2))=−∞limfx→<ln2(x)=limx→<ln2(x+ln(−ex+2))=−∞

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