Math Problem Statement
Question content area top Part 1 Find the following limit or state that it does not exist. ModifyingBelow lim With x right arrow 2 left parenthesis 2 x cubed minus 4 x squared plus 2 x plus 5 right parenthesis
Solution
We need to evaluate the limit:
Step 1: Direct Substitution
Since this is a polynomial function, it is continuous for all real values of . This means we can directly substitute :
Step 2: Compute Each Term
Conclusion
Thus, the limit is:
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Related Questions:
- What is the general rule for finding the limit of a polynomial function?
- How does continuity help in evaluating limits?
- What happens when direct substitution leads to an indeterminate form?
- How do you evaluate limits of rational functions?
- What techniques can be used if direct substitution fails?
Tip: Always check for direct substitution first when evaluating limits, especially for polynomial functions!
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Math Problem Analysis
Mathematical Concepts
Limits
Polynomial Functions
Continuity
Substitution Method
Formulas
lim_{x→a} f(x) = f(a) for continuous functions
Theorems
Continuity Theorem
Direct Substitution Theorem
Suitable Grade Level
Grades 10-12