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

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.

no solution

step-by-step explanation:

there is not enough information in the problem to solve.