SOLUTION: I keep getting 0 as my answer for this problem, but the answer key says 1/2. Any help would be greatly appreciated!! Problem: Limit as x is approaching 0 of { {sqrt ( 1+x ) -1 }

Question 989973: I keep getting 0 as my answer for this problem, but the answer key says 1/2. Any help would be greatly appreciated!!
Problem: Limit as x is approaching 0 of { {sqrt ( 1+x ) -1 } / ( x ) }
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
Do you know and did you learn that

= + the terms of lower orders of magnitude at   x ---> 0 ?

In any case, it is so.

Therefore, = + the terms of lower orders of magnitude at   x ---> 0,     and further

= + the terms of lower orders of magnitude at   x ---> 0.

It implies that lim = at   x ---> 0.

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