lim-x-sin1-1-x-2-1-cosx-

Question Number 200795 by mathlove last updated on 23/Nov/23

\lim_{x \to s i n 1} \frac{1 - x^{2}}{1 + c o s x} = ?

Answered by witcher3 last updated on 23/Nov/23

x \to \frac{1 - x^{2}}{1 + \cos (x)} is defined in \sin (1)

Commented by mathlove last updated on 23/Nov/23

i s s i n 1 \approx 0 ?

Commented by witcher3 last updated on 23/Nov/23

\frac{π}{4} < 1 < \frac{π}{3}

\frac{1}{\sqrt{2}} < \sin (1) < \frac{\sqrt{3}}{2}

Commented by Frix last updated on 23/Nov/23

Even if \sin 1 ° is a very small number {it}^{'} s

still \neq 0 . We use exact values . x \to \sin 1 ° does

not mean x \to 0 . Even x \to \frac{1}{10^{1000000}} does not

mean x \to 0 .

Commented by Frix last updated on 23/Nov/23

Even with x \to 0 we get \frac{1 - 0^{2}}{1 + \cos 0} = \frac{1}{2} . No use

to calculate a limit .

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