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

Find all the real solutions to cubic equation, Find all the real solutions ...

Find all the real solutions to cubic equation x^3 + 4x^2 - 10 =0. Use the cubic equation x^3 + 4x^2 - 10 =0 and perform the following call to the bisection method [0, 1, 30] Use

Cylindrical coordinate system, how to describe the locus of the equation x^...

how to describe the locus of the equation x^2+6xy+y^2+z^2=1 in cylindrical polar coordinates?

Logs, the variables x and y are thought to be related by a law of the form ...

the variables x and y are thought to be related by a law of the form ay^2=(x+b)lnx Where a and b are unknown constants. Can a and b be found and how.

Find the distance of the bird from the girl, A boy standing on a horizontal...

A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an elevation of 300. A girl standing on the roof of 20 meter high building finds the angl

Math, i have problems with math and my teacher said that i am still progres...

i have problems with math and my teacher said that i am still progressing in math

Extended product rule, Extended product rule : As a last topic let's note ...

Extended product rule : As a last topic let's note that the product rule can be extended to more than two functions, for instance.  ( f g h )′ = f ′ gh + f g ′ h+ f g h′ ( f

Whats this, how do you determine if a graph has direct variation

how do you determine if a graph has direct variation

the comic book, a) The first comic book is of shakitman was sold in 1938. ...

a) The first comic book is of shakitman was sold in 1938. In 2010, the estimated price for this comic book in good condition was about $500,000. This represented a return of 25 per

3-d geometry, Q) In 3D-geometry give + and - signs for x,y,z, in all eight ...

Q) In 3D-geometry give + and - signs for x,y,z, in all eight octants Ans) There is no specific hard rule for numbering the octants. So, it makes no real sense to ask which octan

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