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 $\lim_{{x \to c}} [f(x) - g(x)] = L - M$.
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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?
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 $\lim_{x \to c} [\frac{f(x)}{g(x)}] = \frac{\lim_{x \to c} f(x)}{\lim_{x \to c} g(x)}$.