## Calculus with Applications (10th Edition)

The function $f(x)$ is discontinuous at $x=1$, (a) $$f(1) =2$$ . (b) $$\lim _{x \rightarrow-1^{-}} f(x)=-2$$ (c) $$\lim _{x \rightarrow-1^{+}} f(x)=-2$$ (d) Since $$\lim _{x \rightarrow-1^{-}} f(x)=\lim _{x \rightarrow-1^{+}} f(x)=-2$$ then, $$\lim _{x \rightarrow-1} f(x)=-2$$ (e) $$\lim _{x \rightarrow-1} f(x) \ne f(1).$$
The function $f(x)$ is discontinuous at $x=1$, (a) $$f(1) =2$$ . (b) $$\lim _{x \rightarrow-1^{-}} f(x)=-2$$ (c) $$\lim _{x \rightarrow-1^{+}} f(x)=-2$$ (d) Since $$\lim _{x \rightarrow-1^{-}} f(x)=\lim _{x \rightarrow-1^{+}} f(x)=-2$$ then, $$\lim _{x \rightarrow-1} f(x)=-2$$ (e) $$\lim _{x \rightarrow-1} f(x) \ne f(1).$$