I don't understand how to remove the discontinuity on this problem:

(x-4)/( (sq. root of x) - 2), x=4

please help!

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- September 28th 2008, 02:02 PMh4hv4hd4si4nCalc hmwk- extend the fucntion and remove discontinuity
I don't understand how to remove the discontinuity on this problem:

(x-4)/( (sq. root of x) - 2), x=4

please help! - September 28th 2008, 02:14 PMMoo
- September 28th 2008, 06:10 PMh4hv4hd4si4n
I'm sorry, I don't think I asked the right question, here goes: is x=4 the extended function?

- September 29th 2008, 11:16 AMMoo
- September 29th 2008, 11:41 AMSoroban
Hello, h4hv4hd4si4n!

Quote:

Remove the discontinuity: .

Since , there is a discontinuity atCode:`|`

| *

| *

| o

| * :

| * :

|* :

| :

2* :

| :

| :

----+------+-------------

| 4

. . with a hole at (4, 4).

Rationalize: .

Hence: .

Therefore: .

. . and this "fills in the hole" . . . The function is continuous.