1. The problem statement, all variables and given/known data Find limit L. Then find δ > 0 such that |f(x) - L| < 0.01 Limit when x approaches 2 of x^2 -3 2. Relevant equations 0 < |x-c| < δ 0 < |f(x) - L| < ε 3. The attempt at a solution function is continuous at D = ℝ so limit is f(2) = 1 0 < |x-2| < δ and 0 < |x^2 -3 -1| < 0.01 ⇔ 0 < |x^2 -4| <0.01 ⇔ 0 < |x + 2|*|x-2| < 0.01 which is good because: 0 < |x-2| = 0.01 / |x+2| I've seen the solution and i see that i'm supposed to assume a range for x (like (1,3) ). I can imagine that because the function isn't linear a range has to be assumed. They say that assuming this range gives δ = 0.01 / 5 = 0.002 witch seems to be the smallest of 0.01 / 3 and 0.01 / 5. That makes sense to me. But why this chosen range? Why does this range apply to ε = 0.01? Choosing a different range gives a different δ. Who can help me with this i'm really trying to understand this.