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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

Yeah psymon