Hi Melody,
thank you for $$\pm\infty$$.
Now to the limits:
\prod\limits_{i=1}^n x_i
$$\prod\limits_{i=1}^n x_i$$
\sum\limits_{i=1}^n i
$$\sum\limits_{i=1}^n i$$
\lim\limits_{ n \to \infty }x_n
$$\lim\limits_{ n \to \infty }x_n$$
\int\limits_{x=0}^{x=1}
$$\int\limits_{x=0}^{x=1}$$
\frac{40}{(1/10)} $$\frac{40}{(1/10)}$$ ?
$$\frac{40}{\big(1/10\big)}$$
\frac{40}{\big(1/10\big)}
Bye
The quotient of 40/x is undefined. In my opinion I believe the answer should be zero, because how many forties are in zero? Zero.
Anonymous is correct, it is undefined.
To see this, assume we have 40/0.
So we're asking ourselves, what thing can we multiply by 0 to get 40??
Answer, there isn't anything. 0 times any number = 0.
let x=1: $${\frac{{\mathtt{40}}}{{\mathtt{1}}}} = {\mathtt{40}}$$
let x=$$\frac{1}{10}$$=0.1: $${\frac{{\mathtt{40}}}{\left({\frac{{\mathtt{1}}}{{\mathtt{10}}}}\right)}} = {\mathtt{400}}$$
latex code: \frac{1}{10}
let x=$$\frac{1}{1000}$$=0.001: $${\frac{{\mathtt{40}}}{\left({\frac{{\mathtt{1}}}{{\mathtt{1\,000}}}}\right)}} = {\mathtt{40\,000}}$$
latex code: \frac{1}{1000}
let x=$$\frac{1}{10000000000}$$=0.0000000001: $${\frac{{\mathtt{40}}}{\left({\frac{{\mathtt{1}}}{{\mathtt{10\,000\,000\,000}}}}\right)}} = {\mathtt{400\,000\,000\,000}}$$
latex code: \frac{1}{10000000000}
let x=$$\frac{1}{100000000000000000000}$$=0.00000000000000000001:$${\frac{{\mathtt{40}}}{\left({\frac{{\mathtt{1}}}{{\mathtt{100\,000\,000\,000\,000\,000\,000}}}}\right)}} = {\mathtt{4\,000\,000\,000\,000\,000\,000\,000}}$$
latex code: \frac{1}{100000000000000000000}
...
let x=0=0.0000000000000000...: $$\boxed{\frac{40}{0}=\infty}$$
latex code: \boxed{\frac{40}{0}=\infty}
40/x if x=0 is infinite!
Hi Heureka,
You have an excellent argument.
BUT
what if you start with $$x=\dfrac{40}{(\frac{-1}{10})}\\\\$$ and then continue with a similar argument to yours.
I think that you end up with $$\frac{40}{0}=\:-\infty$$
It can't equal $$-\infty \quad and \quad +\infty$$ at the same time therefore it is undefined.
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I really need to learn to write limits using Latex!
also
\frac{40}{(1/10)}
$$\frac{40}{(1/10)}$$
How did you get it to write the fraction upright on the bottom more neatly than mine?
I had to go into display mode else it was too squashy.
Thank you.
Hi Melody,
thank you for $$\pm\infty$$.
Now to the limits:
\prod\limits_{i=1}^n x_i
$$\prod\limits_{i=1}^n x_i$$
\sum\limits_{i=1}^n i
$$\sum\limits_{i=1}^n i$$
\lim\limits_{ n \to \infty }x_n
$$\lim\limits_{ n \to \infty }x_n$$
\int\limits_{x=0}^{x=1}
$$\int\limits_{x=0}^{x=1}$$
\frac{40}{(1/10)} $$\frac{40}{(1/10)}$$ ?
$$\frac{40}{\big(1/10\big)}$$
\frac{40}{\big(1/10\big)}
Bye