Infinity * 0

Calculus Level 1

$\begin{aligned} f(x)=x,\ \ g(x)&=\dfrac{2}{x^3}\\\\\\ \lim_{x\to \infty} f(x)g(x)&=\, ? \end{aligned}$

0 1 2 Undefined

3 solutions

Aniruddha Sanyal
Feb 23, 2020

Go for L'Hospital's Rule with infinity/infinity form

Anon Ymous
Oct 28, 2020

In the example given, in the function g(X),[x^3] grew two orders of magnitude faster than f(X)[x]. Now the very notion of calculating the limit of (X->infinity)/(y->0) is grounded upon the idea that the value to which it tends to is either infinitesimal; the function simply tends to 0; or it grows exponentially; i.e. g(X) [1/(x^3)] & f(X)[x^4], g(X) -> 0 & f(X) -> infinity, f(X)/g(X) -> infinity. I would think it was a singularity given that neither anything/0 = X nor infinity/anything = X, it's not possible to calculate a single value for X. Therefore, there are no meaningful solutions, it entirely depends on the function given . Correct me if I'm wrong, I only wish to learn. Of course for your question itself, it is ambiguous what you are asking. The example you give is intuitive but the way you made the thread made me think more abstractly... Infinity*0 is most certainly a singularity.

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Isaiah Currie - 6 months, 2 weeks ago

😭😭😭 government school and so quite tough to understand english words ........

Dj Devil - 3 months ago

Parul Gupta
May 20, 2018

$f(x)*g(x)=x*2/x^3=2/x^2$
Its limit, as x tends to $\infty$ , is zero.

This makes no sense.

Isaiah Currie - 6 months, 2 weeks ago

0 X infinity is 0, but technically you cant do the problem, so some says its undefined. Technically its undifined UNLESS your not aware of the Zero Property.

(STUDENT) Brody Ritter - 3 months, 2 weeks ago

Infinity * 0

3 solutions

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