If x=0, what is the qotient of 40/x?

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.

Thank you for the LaTex Heureka.