key term - Difference law for limits

Definition

The Difference Law for Limits states that the limit of the difference of two functions is equal to the difference of their 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 Difference Law for Limits can be applied when both individual limits exist.
2. It simplifies complex limit calculations by breaking them into simpler parts.
3. This law holds true regardless of whether the limits are finite or infinite.
4. If either individual limit does not exist, the Difference Law cannot be applied directly.
5. Combining this law with other limit laws like Sum and Product Laws can solve more complex problems.

Review Questions

Related terms

Sum Law for Limits: The Sum Law for Limits states that the limit of the sum of two functions is equal to the sum of their limits: $\lim_{{x \to c}} [f(x) + g(x)] = \lim_{{x \to c}} f(x) + \lim_{{x \to c}} g(x)$.

Product Law for Limits: The Product Law for Limits states that the limit of the product of two functions is equal to the product of their limits: $\lim_{{x \to c}} [f(x) \cdot g(x)] = \lim_{{x \to c}} f(x) \cdot \lim_{{x \to c}} g(x)$.

Quotient Law for Limits: The Quotient Law for Limits states that if $\lim_{x \to c} g(x) \neq 0$, then $\lim_{x \to c} [\frac{f(x)}{g(x)}] = \frac{\lim_{x \to c} f(x)}{\lim_{x \to c} g(x)}$.