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mlazos
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Homework Statement
If [tex]a>>b[/tex] is it correct to say that [tex]\frac{b}{a} \rightarrow 0[/tex]
Can we prove it with limits?
Proving expression with limits
- Thread starter mlazos
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- Expression Limits
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SUMMARY
The discussion centers on proving the limit expression \(\frac{b}{a} \rightarrow 0\) under the condition that \(a >> b\). Participants confirm that as \(a\) approaches infinity, the limit of \(\frac{b}{a}\) indeed approaches 0, based on the principle that any finite number divided by an infinitely large number results in 0. The key takeaway is that the relationship \(a >> b\) suffices to conclude that \(\frac{b}{a}\) approaches 0 as \(a\) increases without bound.
PREREQUISITES- Understanding of limits in calculus
- Familiarity with the concept of infinity in mathematical analysis
- Basic algebraic manipulation of fractions
- Knowledge of asymptotic notation and relationships
- Study the formal definition of limits in calculus
- Explore the concept of asymptotic behavior in mathematical analysis
- Learn about epsilon-delta proofs for limits
- Investigate the implications of limits in real-world applications
Students studying calculus, mathematicians interested in limit proofs, and educators teaching concepts of infinity and limits in mathematics.
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