What is #lim x->0# of #((sqrt(1+sinx) -1) / (x))#?

1 Answer
Cesareo R.
Oct 6, 2016

#1/2#

Explanation:

#(sqrt(1+sinx) -1) / (x)= ((sqrt(1+sinx) -1)(sqrt(1+sinx) +1)) /( x(sqrt(1+sinx) -1)) = (1+sinx-1)/( x(sqrt(1+sinx) +1)) = sin x/x 1/(sqrt(1+sinx) +1)#

so

#lim_(x->0)(sqrt(1+sinx) -1) / (x) = lim_(x->0)sin x/x 1/(sqrt(1+sinx) +1) =1 cdot 1/2 = 1/2#

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