Indeterminate forms, Mathematics

Assignment Help:

Indeterminate forms

Limits we specified methods for dealing with the following limits.

967_limit41.png

In the first limit if we plugged in x = 4 we would get 0/0 & in the second limit if we "plugged" within infinity we would get ∞ /-∞ (recall that as x goes to infinity polynomial will act in the similar fashion that its largest power behaves). Both are called indeterminate forms.  In both cases there are competing interests or rules & it's not clear which will win out.

In the case of 0/0 typically we think of a fraction which has a numerator of zero as being zero. Though, we also tend to think of fractions wherein the denominator will zero as infinity or may not exist at all.  Similarly, we tend to think of a fraction wherein the numerator & denominator are the similar as one.  Therefore, which will win out?  Or will neither win out and they all will "cancel out" and the limit will attain some other value?

In the case of ∞ /-∞ we contain a similar set of problems.  If the numerator of fraction will be infinity we tend to think of the whole fraction will be infinity.  Also if the denominator will be infinity we tend to think of the fraction will be zero. We also have the case of a fraction wherein the numerator & denominator are the similar (ignoring the minus sign) and thus we might get -1.  Again, it's not apparent which of these will win out, if any will win out.

Along the second limit there is the further problem which infinity isn't actually a number and therefore we actually shouldn't even treat it as a number.  Most of time it simply won't behave as we would expect it to if it was a number.

It is the problem with indeterminate forms.  It's just not apparent what is happening in the limit. There are other kinds of indeterminate forms as well. Some other kinds are following,

(0) ( ± ∞ )         1       00                 ∞0            ∞ - ∞

2118_limit42.png

These all contain competing interests or rules which tell us what have to happen and it's just not apparent which, if any, of the interests or rules will win out.

For the two limits above we work on them as follows.

1234_limit43.png

In the first case simply we factored, canceled & took the limit and in the second case we factored out an x2 from both the numerator & the denominator and took the limit. Notice that none of the competing interests or rules in these instance won out! That is frequently the case.

Thus we can deal with some of these.  Though what about the following two limits.

29_limit44.png

First is a 0/0 indeterminate form, however we can't factor this one.  The second is an  ∞ /∞   indeterminate form, however we can't just factor an x2 out of the numerator.


Related Discussions:- Indeterminate forms

Correlation, How o make vicariate frequency distribution table

How o make vicariate frequency distribution table

Objective functions, For schedule consistency, you decide to require each o...

For schedule consistency, you decide to require each officer to report for their eight-hour shift at 12 AM, 4 AM, 8 AM, 12 PM, 4 PM, or 8 PM. As the Director of Public Safety, you

Determine the head loss, A 3 km pipe starts from point A end at point B ...

A 3 km pipe starts from point A end at point B Population = 3000 people Q = 300 L/day/person Roughness = cast ion pipe Length of the pipe = 3km Case 1 From A to B

Cross product - vector, Cross Product In this last section we will loo...

Cross Product In this last section we will look at the cross product of two vectors.  We must note that the cross product needs both of the vectors to be three dimensional (3D

What fraction of water flows out, A conical vessel of radius 6cm and height...

A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just im

Conversion\, how many mg are there in g?

how many mg are there in g?

The normal approximation to the binomial , A certain flight arrives on time...

A certain flight arrives on time 78% of the time. Suppose 1000 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

Calculus, I need help fast with my calculus work

I need help fast with my calculus work

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd