Question

Find the limit f(x),if it exists.sketch the graph of f(x).

Limit x approaching zero f(x),where f(x)=2-x,x less than or equal zero,. x+2, x>0

Answer 1

$$\lim\limits_{x\to0^-}f(x)=\lim\limits_{x\to0^-}(2-x)=2-0=2$$

$$\lim\limits_{x\to0^+}f(x)=\lim\limits_{x\to0^+}(x+2)=0+2=2$$

Since $\lim\limits_{x\to0^-}f(x)=2=\lim\limits_{x\to0^+}f(x),$ then $\lim\limits_{x\to0}f(x)$ exists, and

$$\lim\limits_{x\to0}f(x)=2$$