Let f(x)=8x. In order to prove that the limit as x approachs 1 exists, find Delta >0 for a given epsilon ?

Question

Let f(x)=8x. In order to prove that the limit as x approaches +1 exists, find Delta >0 for a given epsilon= 0.05

(Hint: use the formal definition of limit in this problem.)

Answer 1

The limit is 8.

|8x - 8| < .05

8|x-1| < .05

|x-1| < .00625

So that's your delta: .00625