How Can We Rewrite the Limit and Continuity Equation Lim(x-->0) x/a[b/x]?

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The limit and continuity equation Lim(x-->0) x/a[b/x] can be expressed as x/a(b/x - {b/x}). The discussion clarifies the use of square brackets, which denote the greatest integer function, and curly brackets, which indicate the fractional part of a variable. The equation Lim(x-->0) (b/x - b/a({b/x}/{b/x})) is analyzed, highlighting that {b/x}/{b/x} equals 1. The participants emphasize the importance of understanding these notations for accurate mathematical interpretation.

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  • Basic algebraic manipulation of fractions
  • Knowledge of continuity concepts in mathematical analysis
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  • Explore the greatest integer function and its applications
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Students and educators in mathematics, particularly those focusing on calculus and analysis, as well as anyone seeking to clarify the use of mathematical notation in limits and continuity.

Kartik.
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Lim(x-->0) x/a[b/x] can be written as x/a(b/x-{b/x})

how can we write this as
lim(x-->0)
(b/x -b/a({b/x}/{b/x}))?
 
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Do [square] and {curly} brackets have some special meaning to you? Because
\lim_{x \to 0} \frac{a}{x} \frac{b}{x} \neq \frac{x}{a} \left( \frac{b}{x} - \frac{b}{x} \right)
doesn't really make sense to me.
 
CompuChip said:
Do [square] and {curly} brackets have some special meaning to you? Because
\lim_{x \to 0} \frac{a}{x} \frac{b}{x} \neq \frac{x}{a} \left( \frac{b}{x} - \frac{b}{x} \right)
doesn't really make sense to me.

Sorry, they are very common in my exercise books
square brackets mean the greatest integer value of the variable within and the curly brackets mean the fractional part of the variable within.
 
Kartik. said:
Lim(x-->0) x/a[b/x] can be written as x/a(b/x-{b/x})

how can we write this as
lim(x-->0)
(b/x -b/a({b/x}/{b/x}))?

Your question is a little confusing. You have a term {b/x}/{b/x} (=1??). So it seems you are asking about (b/x - b/a)?
 

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