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 P: 94 I am having trouble understanding how to find the limit of a function (using the definition of a limit). I have a class example, and was wondering if anyone could walk me through the steps. 1. The problem statement, all variables and given/known data Using the definition of the limit to show that limx→2(x2)=4 f(x) = x2 c=2 L=4 Given an arbitrary ε>0, take δ=min{1,ε/5} If x≠2 and |x-2|<δ then |x-2|<1 and |x-2|< ε/5 |f(x)-L| = |x2-4| = |(x-2)(x+2)| = |x-2||x+2| |x-2|<1 => 1 3 |x+2|<5 |x-2||x+2| < (ε/5)(5) = ε so |f(x)-L|<ε 2. Relevant equations We say that lim f(x)x→c=L if: $\forall$ε>0 $\exists$δ>0 $\forall$x$\in$dom f if x≠c and |x-c|<δ then |f(x)-ε|