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
- The Difference Law for Limits can be applied when both individual limits exist.
- It simplifies complex limit calculations by breaking them into simpler parts.
- This law holds true regardless of whether the limits are finite or infinite.
- If either individual limit does not exist, the Difference Law cannot be applied directly.
- Combining this law with other limit laws like Sum and Product Laws can solve more complex problems.
Review Questions
- What is the Difference Law for Limits, and how is it mathematically expressed?
- Can you apply the Difference Law if one of the individual function limits does not exist? Explain.
- How would you use the Difference Law in conjunction with other Limit Laws to solve a problem?
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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 $\lim_{x \to c} [\frac{f(x)}{g(x)}] = \frac{\lim_{x \to c} f(x)}{\lim_{x \to c} g(x)}$.
