Lim x → 2 (x3 − 3x + 3) = 5 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1

is to say that for any , we can find that guarantees





Observing that , the polynomial remainder theorem tells us that we can factorize the cubic to get



If we assume , we can set up a corresponding upper bound on the quadratic factor. We start with , from which we have



Now,



which suggests that we can choose to ensure that we arrive at the inequality .

So, given , we would have



If , we would take

0=6x+2y+10 is equivalent to the simplified form: y= -3x - 5• parallel lines always have the same slope, different y intercept knowing this, we can say the slope, or m of the line parallel to y= -3x - 5 is -3.m= -3 hope this could !