Indeterminate form, Mathematics

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.

Posted Date: 4/11/2013 5:40:30 AM | Location : United States







Related Discussions:- Indeterminate form, Assignment Help, Ask Question on Indeterminate form, Get Answer, Expert's Help, Indeterminate form Discussions

Write discussion on Indeterminate form
Your posts are moderated
Related Questions
Q. Define Period, Amplitude and Phase Shift? Ans. Period, amplitude and phase shift are used when describing a sinusoidal curve The period of a function is the smallest

Five years ago a business borrowed $100,000 agreeing to repay the principal and all accumulated interest at 8% pa compounded quarterly, 8 years from the loan date. Two years after

1. Using suffix trees, give an algorithm to find a longest common substring shared among three input strings: s 1 of length n 1 , s 2 of length n 2 and s 3 of length n 3 .

Polynomials In this section we will discuss about polynomials.  We will begin with polynomials in one variable. Polynomials in one variable Polynomials in one variable

love is a parallelogram where prove that is a rectangle

Critical point of exponential functions and trig functions, Let's see some examples that don't just involve powers of x. Example:  find out all the critical points for the


how do i write a conjecture about the sum of two negative integers.

Find the 14th term in the arithmetic sequence. 60, 68, 76, 84, 92

Explain how to Converting Percents to Decimals ? Percent : "Percent" means "per hundred." Percents are represented by a percent sign ( % ) to the right of a number.  For exam