Afunction f(x), a point c, the limit of f(x) as x approaches c, and a positive number ε are given. find a number δ > 0 such that for all x, 0 < |x - c| < δ ⇒ |f(x) - l| < ε. f(x) = - 2x - 6, l = - 12, c = 3, and ε = 0.01

The limit of this function is obviously -12, because the function is actually continuous and we can directly compute it:

So we have . Now, since we want the function and the target to be far no more than 0.01, we have

So, we came to the following conclusion: in order for and the limit to be far no more than 0.01, we need the variable x and its target 3 to be far no more than 0.005. In other words, we're claiming that

so the possibilities of the measurement of the side of the triangle are either it is longest side or not the longest side

when it is the longest side

s < 25 + 35s < 60

if it is not the longest side

35 < 25 + s10 < sso 10 < s < 60so the perimeter70 < p < 130

the answer would be 0.54