Math Problem Statement
Solution
Given that:
we need to determine:
Let's analyze this problem step-by-step.
Step 1: Understanding the Limit Condition
The limit of a function as is given by:
This implies that as approaches 2, the value of approaches 4. To avoid an indeterminate form, the numerator must balance with the denominator . As , the denominator approaches .
Step 2: Setting Up the Equation
If approaches 2, then:
Simplifying the denominator, we get:
Step 3: Solving for
Simplifying:
Adding 1 to both sides:
Dividing by 3:
Final Answer
Would you like more details or have any further questions?
Related Questions
- How can you verify if a limit exists for a given function?
- What happens if was undefined? How would the result change?
- How do you apply L'Hospital's Rule to solve limits like this?
- How would the result change if the limit was ?
- Can we generalize this method for other types of rational limits?
Tip
When dealing with limits of rational functions, always check if the numerator and denominator both approach zero or infinity to decide if L'Hospital's Rule can be applied.
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Math Problem Analysis
Mathematical Concepts
Limits
Functions
Algebra
Formulas
Limit formula: lim(x → c) f(x)
Solving for f(x) using limits
Theorems
Limit of a function
Suitable Grade Level
Grades 11-12
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