Limit Laws

Learn limit laws for sums, limit laws for quotients.

Lesson 1 of 32 parts Practice Flashcards

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Limit Laws for Sums

Objective: Explain limit laws for sums, apply the stated method, and check its conditions.

If f and g have finite limits L and M at the same target, the sum has limit L+M and a constant multiple cf has limit cL. Apply the laws only when their component limits satisfy the stated existence conditions. Existence assumptions matter; a nonexistent component limit cannot be substituted blindly.

Formulas

$lim(f+g)=lim f+lim g$

Worked examples

Try itIf lim f(x)=42 and lim g(x)=7, both finite at the same target, find lim [f(x)+g(x)].Show answer

Step 1: The sum law applies to existing finite limits. Step 2: Add 42 and 7. Step 3: The limit is 49.

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Limit Laws for Sums

Objective: Explain limit laws for sums, apply the stated method, and check its conditions.

Formulas

$lim(f+g)=lim f+lim g$

Worked examples

Try itIf lim f(x)=42 and lim g(x)=7, both finite at the same target, find lim [f(x)+g(x)].Show answer

Step 1: The sum law applies to existing finite limits. Step 2: Add 42 and 7. Step 3: The limit is 49.

Limit Laws for Quotients

Objective: Explain limit laws for quotients, apply the stated method, and check its conditions.

If finite limits L and M exist and M≠0, then lim(f/g)=L/M. A zero denominator limit requires additional analysis and may give an indeterminate form or unbounded behavior; it cannot be evaluated by the quotient law alone. Do not apply the quotient law with a zero denominator limit.

Formulas

$lim(f/g)=L/M when M≠0$

Worked examples

Try itIf lim f(x)=42 and lim g(x)=7≠0 at the same target, find lim f(x)/g(x).Show answer

Step 1: A nonzero denominator limit allows the quotient law. Step 2: Use 42/7. Step 3: The limit is 6.

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