Find the limit L.Then use the Ɛ -δ definition to prove that L

Question

lim    cubroot of x

x-->0

Answer 1

Step 1:

The expression is

Substitute in the above expression

Step 2:

definition:

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

Consider 

Cubing on both sides.

Consider

Observe the relation between and  .

Hence, .

Solution:

and .