Question #e007a

1 Answer
Jim S
Dec 8, 2017

x>x>-2−2 then lim_(xrarr-2)(3x+6)/|x+2|=3 , x<-2 then lim_(xrarr-2)(3x+6)/|x+2|=-3

Explanation:

  • If x+2>0 <=> x>-2 , x->-2^+ then

lim_(xrarr-2^+)(3x+6)/(|x+2|) = lim_(xrarr-2^+)(3x+6)/(x+2) =
= lim_(xrarr-2^+)3(x+2)/(x+2) = 3lim_(xrarr-2^+)cancel(x+2)/cancel(x+2) <=> 3lim_(xrarr-2^+)1 =3

  • If x+2<0 <=> x<-2 , x->-2^-

lim_(xrarr-2^-)(3x+6)/(|x+2|) = lim_(xrarr-2^-)(3x+6)/-(x+2) =
= -3lim_(xrarr-2^-)cancel(x+2)/cancel(x+2) =-3*1=-3

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