3 Cases for solving limits approaching infinity.
Case 1: Smaller Order Polynomial in Numerator
• Divide everything by largest exponent
• Simplify
• Limits of this type will always be zero.
Case 2: Equal Order Denominator and Numerator
•Divide by exponent
• Simplify
• Limits of this type will always be the simplified quotient of the leading coefficients of numerator and denominator.
Case 3: Larger Polynomial in Numerator
• Divide by exponent in denominator
• Simplify
• Limits of this type will not exist, either giving increasing or decreasing without bound.
Example:
Case 1: Smaller Order Polynomial in Numerator
• Divide everything by largest exponent
• Simplify
• Limits of this type will always be zero.
Case 2: Equal Order Denominator and Numerator
•Divide by exponent
• Simplify
• Limits of this type will always be the simplified quotient of the leading coefficients of numerator and denominator.
Case 3: Larger Polynomial in Numerator
• Divide by exponent in denominator
• Simplify
• Limits of this type will not exist, either giving increasing or decreasing without bound.
Example:
Answer: