Indeterminate form, Mathematics

Assignment Help:

Indeterminate form : The 0/0 we initially got is called an indeterminate form. It means that we don't actually know what it will be till we do some more work.  In the denominator typically zero means it's undefined. Though that will only be true if the numerator isn't also zero.  Also, in the numerator zero usually means that the fraction is zero, unless the denominator is also zero. Similarly anything divided by itself is 1, unless we're talking regarding zero.

Hence, there are actually three competing "rules" here & it's not clear which one will win out.  It's also a chance that none of them will win out & we will get something completely different from undefined, zero, or one. For instance, we might get a value of 4 out of this, to pick a number totally at random.

There are several more kinds of indeterminate forms

Let's check couple of more examples.

Example   Evaluate the given limit.

1478_limit40.png

Solution

In this case we also obtain 0/0 and factoring is not actually an option.  Though, till there is some simplification that we can do.

2053_limit41.png

Hence, upon multiplying out the first term we get a little cancellation and notice that we can factor out an h out of both terms in the numerator that will cancel against the h in the denominator and the division by zero problem goes away & then we can evaluate the limit.

1379_limit42.png

Let's take a look at another type of problem which can arise in computing some limits including piecewise functions.


Related Discussions:- Indeterminate form

Function and relation, how to know if it is function and if is relation

how to know if it is function and if is relation

Linear Systems, Find the solution to the following system of equations usin...

Find the solution to the following system of equations using substitution:

Optimization, Optimization is required in situations that frequentl...

Optimization is required in situations that frequently arise in finance and other areas. Organizations would like to maximize their profits or minimize thei

What is the volume of the frustum, If the areas of the circular bases of a ...

If the areas of the circular bases of a frustum of a cone are 4cm 2 and 9cm 2 respectively and the height of the frustum is 12cm. What is the volume of the frustum. (Ans:44cm 2 )

What is a system of equations?, What is a System of Equations? And its Solu...

What is a System of Equations? And its Solution? Here is an example of a system of equations (also called a simultaneous system of equations) x 2 + y = 3

Find the time required for an enlargement, 1. The polynomial G(x) = -0.006x...

1. The polynomial G(x) = -0.006x4 + 0.140x3 - 0.53x2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase

Complex numbers, Complex Numbers In the radicals section we noted that...

Complex Numbers In the radicals section we noted that we won't get a real number out of a square root of a negative number.  For example √-9 isn't a real number as there is no

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