Mathematics

The key insight is recognizing when direct substitution is safe—that is, when plugging in $x=1$ won't create an undefined expression like $\frac{0}{0}$ or $\frac{k}{0}$. A limit is evaluable by substitution alone if the function is continuous at that point, meaning the numerator and denominator are both well-defined and the denominator is nonzero. Before you check each option, ask yourself: "Does this expression stay defined and finite when I plug in $x=1$?" If yes, substitute; if no, you'll need algebra or another technique first.

The key insight is recognizing when direct substitution is safe—that is, when plugging in $x=1$ won't create an undefined expression like $\frac{0}{0}$ or $\frac{k}{0}$. A limit is evaluable by substitution alone if the function is continuous at that point, meaning the numerator and denominator are both well-defined and the denominator is nonzero. Before you check each option, ask yourself: "Does this expression stay defined and finite when I plug in $x=1$?" If yes, substitute; if no, you'll need algebra or another technique first.