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 }

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> 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 }      Log On


   

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(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Do you know and did you learn that

sqrt%281+%2B+x%29 = 1+%2B+%281%2F2%29x + the terms of lower orders of magnitude at   x ---> 0 ?

In any case,  it is so.

Therefore,  sqrt%281+%2B+x%29-1 = %281%2F2%29x + the terms of lower orders of magnitude at   x ---> 0,     and further

 %28sqrt%281+%2B+x%29-1%29%2Fx = %281%2F2%29 + the terms of lower orders of magnitude at   x ---> 0.

It implies that lim %28sqrt%281+%2B+x%29-1%29%2Fx = 1%2F2 at   x ---> 0.