For the limit lim x → 3 (x3 − 4x + 9) = 24 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (round your answers to four decimal places.)

is to say that for any , there exists such that

Notice that

If we fix , we would have

which is to say we can place a bound on the quadratic term above of 33 so that

This suggests we could set .

So if we're given , we would choose , and if , we would choose .

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !