Question

Prove the statement using the Є, δ definition of a limit and illustrate with a diagram.

Answer 1

Step 1:

The expression is .

definition:

means that for every , there exists a , such that for every , the expression  implies .

Consider .

Adding each side by .

As ,

Step 2:

Consider .

As ,

.

Observe the relation between and  .

Hence,

Step 3:

definition:

change in corresponds to change in .

Consider , then .

Graph:

Therefore, change in corresponds to change in .

Solution:

.