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

Find out a vector that is orthogonal to the plane, A plane is illustrated b...

A plane is illustrated by any three points that are in the plane.  If a plane consists of the points P = (1, 0,0) , Q = (1,1,1) and R = (2, -1, 3) find out a vector that is orthogo

Dynamic and kinematic viscosity , Tabulated values of the dynamic and kinem...

Tabulated values of the dynamic and kinematic viscosity of aqueous sodium chloride solutions have been researched in the academic literature (Kestin et al 1981). The data availab

Determine the average bit rate - huffman codebook, 1. Consider a source wi...

1. Consider a source with 4 symbols {a,b,c,d}. The probability of the 4 symbols are P(a)=0.4, p(b) = 0.1, p(c)=0.2, p(d)= 0.3. a. Design a Huffman codebook for these symbols.

Finding the LCM, what is the LCM of 18, 56 and 104 show working

what is the LCM of 18, 56 and 104 show working

Constant aceleration formulae, a car comes to a stop from a speed of 30m/s ...

a car comes to a stop from a speed of 30m/s in a distance of 804m. The driver brakes so as to produce a decelration of 1/2m per sec sqaured to begin withand then brakes harder to p

Chi-square hypothesis tests as non-parametric test(x2), Chi-square hypothes...

Chi-square hypothesis tests as Non-parametric test(X2) They contain amongst others i.    Test for goodness of fit ii.   Test for independence of attributes iii.  Test

Pressure and vorticity distributions, Normal 0 false false ...

Normal 0 false false false EN-IN X-NONE X-NONE

Lcm, what is the LCM of 4, 6, 18

what is the LCM of 4, 6, 18

How much is the volume increased, If the lengths of all sides of a box are ...

If the lengths of all sides of a box are doubled, how much is the volume increased? a. 2 times b. 4 times c. 6 times d. 8 times d. The volume of a box is taken by mu

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