How to write a widehat(^) symbol and plus-minus in LaTeX?

Question: How to write a widehat(^) plus-minus in $LATEX$?

Answer: It can be written as: $\widehat{fg}$

$$\widehat{fg}$$

Question: How to write plus-minus ($\pm$) in $LATEX$?

Answer: It can be written as: $\lim_{n \to \pm \infty}$

$$\underset{n\to \pm \mathrm{\infty }}{lim}$$