Math Problem Statement
Using: limx→5f(x)=6 and limx→5g(x)=4, evaluate limx→5f(x)+g(x)6f(x). Limit =
Solution
To evaluate the limit of the expression , we can apply the properties of limits, which allow us to evaluate the limit of the numerator and denominator separately.
Given:
Now, applying the limits to the expression:
Step 1: Evaluate the numerator:
Step 2: Evaluate the denominator:
Step 3: Combine the results:
Thus, the limit is:
Would you like further details on any part of the process?
Here are 5 related questions to explore:
- How do you apply limit laws to more complex expressions?
- What happens if a limit involves indeterminate forms, like ?
- How do you handle limits involving infinity?
- Can L'Hopital's Rule be applied to this problem, and why or why not?
- What if the limits for and approached infinity?
Tip: Always check if the limit form is indeterminate before deciding on an evaluation method.
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Math Problem Analysis
Mathematical Concepts
Calculus
Limits
Limit Laws
Formulas
lim(x → a) [f(x) + g(x)] = lim(x → a) f(x) + lim(x → a) g(x)
lim(x → a) [cf(x)] = c * lim(x → a) f(x)
Theorems
Limit laws
Suitable Grade Level
Grades 11-12 (Calculus)