to find limit of this polynomial x-0,

( sqrt(1+tan x)-sqrt(1+sin x) )/x^3,
can i just say, as x -0, sqrt(1+tan x) = 1,
and sqrt(1+sin x)=1

so the numerator will become 0?

Question

to find limit of this polynomial x->0,

( sqrt(1+tan x)-sqrt(1+sin x) )/x^3,
can i just say, as x ->0, sqrt(1+tan x) = 1, 
and sqrt(1+sin x)=1

so the numerator will become 0?

psymon · Answer

Yeah, but it looks like you have an x^3 in the denominator, which would just make it undefined as it goes to 0.

psymon · Answer

$$\frac{ \sqrt{1+tanx}-\sqrt{1+sinx} }{ x ^{3} }$$
Is this correct?

anonymous · Answer

not clear, but it sure as hell is not a polynomial

anonymous · Answer

i think the limit is $\frac{1}{4}$ power series might do it, or maybe l'hopital, but that will be a drag

anonymous · Answer

Yeah psymon