Compute the following limit:
sqrt x+4 -2/x
lim
x-->0
the x+4 is the only thing under the square root.
the answer is .25, but id like to know how to work this out
(sqrt(x+4) -2) /x
L'Hoptials rule:
it is of the form 0/0, so limit equals
1/2sqrt(x+4)= 1/4
Now, the hard way:
multiply numerator and denominator by sqrt(x+4)+2, so limit now is
Lim ((x+4)-4)/x(sqrt(x+4)+2)
= lim 1/sqrt4+2= 1/4