Question

Let $f\left(x\right)=\{\begin{array}{cc}{x}^2& x<1\\ x& 1<x<4\\ 4-x& x>4\end{array}$, then

• A. $\underset{x\to 1^{-}}{lim}f\left(x\right)=1$
• B. $\underset{x\to 1^{+}}{lim}f\left(x\right)=1$
• C. $\underset{x\to 4^{-}}{lim}f\left(x\right)=4$
• D. $\underset{x\to 4^{+}}{lim}f\left(x\right)=4$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\underset{x\to 1^{-}}{lim}f\left(x\right)=1$
B $\underset{x\to 1^{+}}{lim}f\left(x\right)=1$
C $\underset{x\to 4^{-}}{lim}f\left(x\right)=4$

${lim}_{x\to 1^{-}}f\left(x\right)={lim}_{x\to 1^{-}}{x}^2=1$

${lim}_{x\to 1^{+}}f\left(x\right)={lim}_{x\to 1^{+}}x=1$

${lim}_{x\to 4^{-}}f\left(x\right)={lim}_{x\to 4^{-}}x=4$

${lim}_{x\to 4^{+}}f\left(x\right)={lim}_{x\to 4^{+}}4-x=0$