+0  
 
+3
451
4
avatar+1832 

I solved this question that way 

 

 

 

But the answer in the solution manual is 

 

 

 

I don't understand why they made it -x in the denominator 

 Oct 7, 2014

Best Answer 

 #1
avatar+27396 
+13

The original form of the denominator shows it is positive for all values of x (even when x is negative).  Therefore, if you take x outside the square root sign, you must still keep the denominator positive, so if x is negative you must have -x, instead of just x, to keep it positive.

To convince yourself that this is the right thing to do look at the following graph:

limit

 Oct 7, 2014
 #1
avatar+27396 
+13
Best Answer

The original form of the denominator shows it is positive for all values of x (even when x is negative).  Therefore, if you take x outside the square root sign, you must still keep the denominator positive, so if x is negative you must have -x, instead of just x, to keep it positive.

To convince yourself that this is the right thing to do look at the following graph:

limit

Alan Oct 7, 2014
 #2
avatar+95369 
+3

Thank you Alan,

I was really puzzling over that one.  

 Oct 7, 2014
 #3
avatar+1832 
+3

Thank you Alan .. you are brilliant 

 Oct 7, 2014
 #4
avatar+95369 
+8

YES HE IS!!!

 Oct 7, 2014

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