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What-is-the-difference-between-lim-x-2-and-lim-x-2-




Question Number 66285 by Rio Michael last updated on 12/Aug/19
What is the difference between    lim_(x→2^− )   and  lim_(x→2^+ )
Whatisthedifferencebetweenlimx2andlimx2+
Answered by MJS last updated on 12/Aug/19
limit from left respectively right side. the  two limits can be different  lim_(x→2^− )  (1/(x−2)) =−∞  lim_(x→2^+ ) (1/(x−2))=+∞    lim_(x→0^− ) (x^2 )^(1/x)  =+∞  lim_(x→0^+ ) (x^2 )^(1/x)  =0
limitfromleftrespectivelyrightside.thetwolimitscanbedifferentlimx21x2=limx2+1x2=+limx0x2x=+limx0+x2x=0
Answered by GordonYeeman last updated on 12/Aug/19
the limit x→2 consists on taking   arbitrarily close values of 2 (1.99,  1.9999,1.999999...). x→2^+  is basically  the same but those values must be   greater than 2 (2.01, 2.000001, etc).   In the case of x→2^−  they must be  smaller
thelimitx2consistsontakingarbitrarilyclosevaluesof2(1.99,1.9999,1.999999).x2+isbasicallythesamebutthosevaluesmustbegreaterthan2(2.01,2.000001,etc).Inthecaseofx2theymustbesmaller
Commented by Rio Michael last updated on 12/Aug/19
thank you sirs
thankyousirs

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