Math Problem Statement
which of the functions can be extended continuously at x=3
Solution
Let's analyze each of the given functions to determine which can be extended continuously at .
- **Function ( k(x) = \sin\left(\frac{1}{
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Math Problem Analysis
Mathematical Concepts
Limits and Continuity
Piecewise Functions
Trigonometric Functions
Rational Functions
Formulas
Limit of a function as x approaches a value
Continuity at a point: Limit of f(x) as x -> c = f(c)
Theorems
Limit Theorem for Continuity
Squeeze Theorem (for trigonometric limits)
Rational Function Continuity
Suitable Grade Level
Undergraduate Math or Advanced High School (Grades 11-12)
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