Answer to Question #307747 in Calculus for Luna Heart

Question

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}

Answer 1

$1. \lim\limits_ {x\to-1}(x+2)=-1+2=1\\ 2. \lim\limits_ {x\to0}(x-2)=0-2=-2\\ 3. \lim\limits_ {x\to-1-0}(x^2-1)=(-1)^2-1=1-1=0\\ \lim\limits_ {x\to-1+0}((x-1)^2-4)=(-1-1)^2-4=4-4=0\\ 4. \lim\limits_ {x\to1-0}(x^3-1)=1^3-1=1-1=0\\ \lim\limits_ {x\to1+0}(x^2+4)=1^2+4=1+4=5\\$