If lim _(xarrow -12)f(x)=-20 and lim _(xarrow -12)g(x)=12 what is the value of lim _(xarrow -12)[f(x)+g(x)] communication

To find the value of $\lim _{x\rightarrow -12}[f(x)+g(x)]$, we can use the property of limits that states the limit of the sum of two functions is equal to the sum of their limits, provided that both limits exist.<br /><br />Given:<br />$\lim _{x\rightarrow -12}f(x)=-20$<br />$\lim _{x\rightarrow -12}g(x)=12$<br /><br />We can apply the property of limits:<br />$\lim _{x\rightarrow -12}[f(x)+g(x)] = \lim _{x\rightarrow -12}f(x) + \lim _{x\rightarrow -12}g(x)$<br /><br />Substituting the given values:<br />$\lim _{x\rightarrow -12}[f(x)+g(x)] = -20 + 12 = -8$<br /><br />Therefore, the value of $\lim _{x\rightarrow -12}[f(x)+g(x)]$ is -8.