+0

limits involving infinity

+3
451
4
+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

#1
+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:

Oct 7, 2014

#1
+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:

Alan Oct 7, 2014
#2
+95369
+3

Thank you Alan,

I was really puzzling over that one.

Oct 7, 2014
#3
+1832
+3

Thank you Alan .. you are brilliant

Oct 7, 2014
#4
+95369
+8

YES HE IS!!!

Oct 7, 2014