help in maths

suyogya

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what is the result of (approaching infinity)/(approaching zero) ?
I think its approaching infinity, but if it is approaching infinity, then multiplying both sides by approaching zero, it became: (approaching zero) times (approaching infinity) = (approaching infinity), which is contradicting as LHS is an indeterminate form.
 

Jomo

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Why not just try an example?
Let's consider if just the denominator is going to 0.
7/(1/1000000) = 7*1000000 is quite large, 293/(1/1000000000) = 293000000000 is quite large. So a small denominator make a fraction quite large (I am assuming that the numerator is positive). Now if you make the numerator large that too makes the fraction bigger.
Consider for example 22222222222/(1/123456789123456789) = 22222222222(123456789123456789) which is large
 

MarkFL

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The form \(\displaystyle \frac{\infty}{0}\) is not indeterminate, and is equivalent to the form \(\infty\). :)
 

suyogya

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suyogya

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Mar 22, 2019
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7
Why not just try an example?
Let's consider if just the denominator is going to 0.
7/(1/1000000) = 7*1000000 is quite large, 293/(1/1000000000) = 293000000000 is quite large. So a small denominator make a fraction quite large (I am assuming that the numerator is positive). Now if you make the numerator large that too makes the fraction bigger.
Consider for example 22222222222/(1/123456789123456789) = 22222222222(123456789123456789) which is large
i know it should be approaching infinity but what about the contradiction i shown in my question
 

Dr.Peterson

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what is the result of (approaching infinity)/(approaching zero) ?
I think its approaching infinity, but if it is approaching infinity, then multiplying both sides by approaching zero, it became: (approaching zero) times (approaching infinity) = (approaching infinity), which is contradicting as LHS is an indeterminate form.
It's not quite clear what you mean by "both sides" (of what equation?). Please show details.

But multiplying by infinities or indeterminate forms is a good way to get confused. Indeterminate forms by definition are forms that can have more than one value, so they can't really lead to contradictions.
 

MarkFL

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An example of that form is:

\(\displaystyle \lim_{x\to\infty}\frac{x}{\dfrac{1}{x}}\)

Now this is algebraically equivalent to:

\(\displaystyle \lim_{x\to\infty}x^2=\infty\)
 

Jomo

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Have you ever noticed that you can't multiply both sides of an equation by 0 (and get any real results).

For example if you have x/2 = 5 you can multiply both sides by 2 and get a meaningful result of x=10. You can even multiply both sides by 7 and get a meaningful result of (7/2)x = 35. Now if you multiply both sides by 0 you get 0=0.
Why do you want to multiply both sides by approaching 0?
 
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