Which of the following statements correctly defines ?

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Which of the following statements correctly defines lim⁡x→cf(x)=L\displaystyle \lim_{x\to c}f(x)=L? (a) There exists δ>0\delta>0 such that for every ε>0\varepsilon>0, if 0<∣x−c∣<δ0<|x-c|<\delta then ∣f(x)−L∣<ε|f(x)-L|<\varepsilon. (b) For every δ>0\delta>0 there exists ε>0\varepsilon>0 such that if 0<∣x−c∣<δ0<|x-c|<\delta then ∣f(x)−L∣<ε|f(x)-L|<\varepsilon. (c) For every ε>0\varepsilon>0 there exists δ>0\delta>0 such that if 0<∣x−c∣<δ0<|x-c|<\delta then ∣f(x)−L∣<ε|f(x)-L|<\varepsilon. (d) For every ε>0\varepsilon>0 there exists δ>0\delta>0 such that if ∣f(x)−L∣<ε|f(x)-L|<\varepsilon then 0<∣x−c∣<δ0<|x-c|<\delta.

Related theory

Browse the problem library