(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

find the limit as x -> 0 of (sin^2(x))/(x^2)

2. Relevant equations

limit as x -> xo (fx) = L iff for every epsilon (>0) there exists a delta (>0) st if

| x - xo | < delta then |f(x) - L | < epsilon

3. The attempt at a solution

Let epsilon be positive. I believe the limit equals one, so I will proceed there.

then

| (sin^2(x))/x^2 - 1| < epsion if | x | < delta

But | f(x) - 1| <= |1/x^2 - 1| . And this is where I get stuck. If I pick delta to be small, and |x| < delta,

| (f(x)) - 1 | becomes very large, and thus is not being bound by any epsilon.

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# Homework Help: Proof of limit by definition

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