Which one of the following statements correctly expresses the definition of ?

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Which one of the following statements correctly expresses the definition of lim⁡x→∞f(x)=L\displaystyle \lim_{x\to\infty}f(x)=L? (a) For every M>0M>0 there exists ε>0\varepsilon>0 such that ∣f(x)−L∣<ε|f(x)-L|<\varepsilon whenever x>Mx>M. (b) For every ε>0\varepsilon>0 there exists M>0M>0 such that ∣f(x)−L∣<ε|f(x)-L|<\varepsilon whenever x>Mx>M. (c) For every ε>0\varepsilon>0 there exists M>0M>0 such that ∣f(x)−L∣<ε|f(x)-L|<\varepsilon whenever x<Mx<M. (d) For every ε>0\varepsilon>0 there exists M>0M>0 such that f(x)−L<εf(x)-L<\varepsilon whenever x>Mx>M.

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