Sum law for limits

Definition

The Sum Law for Limits states that the limit of the sum of two functions is equal to the sum of their individual limits. Mathematically, if $\lim_{{x \to c}} f(x) = L$ and $\lim_{{x \to c}} g(x) = M$, then $\lim_{{x \to c}} [f(x) + g(x)] = L + M$.

5 Must Know Facts For Your Next Test

1. The Sum Law for Limits can be applied to both finite and infinite limits.
2. It is one of the basic limit laws used to simplify complex limit problems.
3. The law holds true regardless of whether the individual limits exist as finite numbers or approach infinity.
4. If either function does not have a limit at a certain point, the Sum Law cannot be applied at that point.
5. This law also extends to sums involving more than two functions: $\lim_{{x \to c}} [f(x) + g(x) + h(x)] = L + M + N$.

Review Questions

• State the Sum Law for Limits in your own words.
• Is it possible to apply the Sum Law for Limits if one of the functions does not have a limit? Why or why not?
• How would you apply the Sum Law for Limits to evaluate $\lim_{{x \to c}} [2f(x) + 3g(x)]$?

Related terms

Limit: The value that a function approaches as the input approaches some value.

Difference Law for Limits: States that the limit of the difference of two functions is equal to the difference of their individual limits.

Product Law for Limits: States that the limit of the product of two functions is equal to the product of their individual limits.