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Question Number 88985 by jagoll last updated on 14/Apr/20

lim_(x→3)  ln ∣x−3∣   exist or no?

limx3lnx3existorno?

Commented by mr W last updated on 14/Apr/20

no.

no.

Commented by jagoll last updated on 14/Apr/20

because   lim_(x→3)  ln ∣x−3∣ = −∞ sir

becauselimx3lnx3=sir

Commented by mr W last updated on 14/Apr/20

yes

yes

Commented by mr W last updated on 15/Apr/20

−∞ or +∞ is not a value! when you  write lim_(x→a) f(x)=∞, it means in daily  language that there is no limit.  because  the function can′t go close to a value.    this is the same as when you say that  you still have money even when the  numver of money you have is zero.

or+isnotavalue!whenyouwritelimxaf(x)=,itmeansindailylanguagethatthereisnolimit.becausethefunctioncantgoclosetoavalue.thisisthesameaswhenyousaythatyoustillhavemoneyevenwhenthenumverofmoneyyouhaveiszero.

Commented by mr W last updated on 15/Apr/20

Commented by mr W last updated on 15/Apr/20

this is for the first day when lerning  about limit.

thisisforthefirstdaywhenlerningaboutlimit.

Commented by malwaan last updated on 15/Apr/20

lim_(x→3^+ )  ln∣x−3∣ = −∞  lim_(x→3^− )  ln∣x−3∣ = −∞  ⇒ lim_(x→3)  ln∣x−3∣ = −∞  (so limit exist)or no ???

limx3+lnx3=limx3lnx3=limx3lnx3=(solimitexist)orno???

Commented by john santu last updated on 15/Apr/20

yes. i agree.  lim_(x→3)  ln ∣x−3∣ ⇒exist

yes.iagree.limx3lnx3exist

Commented by jagoll last updated on 15/Apr/20

i also think like that.  by definition if   lim_(x→a^+ )  f(x) = lim_(x→a^− )  f(x)   then lim_(x→a)  f(x) exist

ialsothinklikethat.bydefinitioniflimxa+f(x)=limxaf(x)thenlimxaf(x)exist

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