Question #307747

Determine whether if lim f(c) = f(c)


x→c



1. f(x) = x+2; c = -1



2. f(x) = x-2; c = 0




3. (at c = -1 )



f(x) = {x ² - 1 if x < -1}



f(x) = { (x - 1) ² - 4 if x ≥ -1}





4. (at c = 1 )



f(x) = {x³ - 1 if x < 1}



f(x) = { x² + 4 if x ≥ 1}




1
Expert's answer
2022-03-08T23:56:16-0500

1.limx1(x+2)=1+2=12.limx0(x2)=02=23.limx10(x21)=(1)21=11=0limx1+0((x1)24)=(11)24=44=04.limx10(x31)=131=11=0limx1+0(x2+4)=12+4=1+4=51. \lim\limits_ {x\to-1}(x+2)=-1+2=1\\ 2. \lim\limits_ {x\to0}(x-2)=0-2=-2\\ 3. \lim\limits_ {x\to-1-0}(x^2-1)=(-1)^2-1=1-1=0\\ \lim\limits_ {x\to-1+0}((x-1)^2-4)=(-1-1)^2-4=4-4=0\\ 4. \lim\limits_ {x\to1-0}(x^3-1)=1^3-1=1-1=0\\ \lim\limits_ {x\to1+0}(x^2+4)=1^2+4=1+4=5\\


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