For the limit

Question

lim 
x → 3 
(x3 − 5x + 3) = 15 

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.) 



ε = 0.2 δ = ? 
ε = 0.1 δ = ?

 

 

Answer 1

The definition of the limits

Let f(x) be a function defined on an interval that contains x = a, except possibly at x = a. 

Then we say that,

"For any ,there is a so that when "

 

The value that x  approaches ," a " is 3.

The limit L  is 15

when

We need to bound |x + 1| and |x + 2|

So if we first fix |x - 3|< 0.2

Then

and

Answer 2

Continuous..

Solution

.