prove-that-0-0-1-

Question Number 184159 by Davidtim last updated on 03/Jan/23

p r o v e t h a t 0^{0} = 1

Commented by Frix last updated on 03/Jan/23

Prove that the moon is a star .

Answered by cortano2 last updated on 03/Jan/23

l e t 0^{n} = x

0^{0} = 0^{n - n} = \frac{0^{n}}{0^{n}} = \frac{x}{x} = 1

Commented by Frix last updated on 03/Jan/23

\frac{0}{0} is not defined .

Let f (0) = g (0) = 0

\lim_{x \to 0} \frac{f (x)}{g (x)} = \lim_{x \to 0} \frac{f^{'} (x)}{g^{'} (x)} which can be any real number

i . e .

\lim_{x \to 0} \frac{x^{2}}{\sin x} = \lim_{x \to 0} \frac{2 x}{\cos x} = 0

\lim_{x \to 0} \frac{x}{x^{2}} = \lim_{x \to 0} \frac{1}{2 x} not defined

\lim_{x \to 0} \frac{x \cos x}{x + \sin x} = \lim_{x \to 0} \frac{\cos x - x \sin x}{1 + \cos x} = \frac{1}{2}

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