Computing limits , Mathematics

Assignment Help:

Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for which it won't work easily.  The reason of this section is to build up techniques for dealing with some limits that will not let us to just use this fact.

Let's firstly got back & take a look at one of the first limits which we looked at and calculate its exact value and verify our guess for the limit.

Example   Evaluate the given limit.

1884_limit36.png

Solution: Firstly let's notice that if we attempt to plug in x= 2 we get,

804_limit37.png

hence, we can't just plug in x = 2 to evaluate the limit .hence, we're going to have to do something else.. 

The first thing which we have to always do while evaluating limits is to simplify the function as much as possible.  In this case that means factoring the numerator and denominator both.  Doing this gives,Hence, upon factoring we saw that we could cancel an x - 2 from the numerator and the denominator both.  Upon doing this now we have a new rational expression which we can plug into since we lost the division by zero problem.  Thus, the limit is,

851_limit38.png

Note that it is in fact what we guessed the limit to be.

2302_limit39.png


Related Discussions:- Computing limits

Repeated eigenvalues, It is the last case that we require to take a look at...

It is the last case that we require to take a look at. During this section we are going to look at solutions to the system, x?' = A x? Here the eigenvalues are repeated eigen

What is trigonometric ratios, What is Trigonometric Ratios ? Trigonome...

What is Trigonometric Ratios ? Trigonometry, a branch of mathematics, is based on the ratios known as sine, cosine, and tangent. Trigonometric ratios apply only to right trian

Initial recognition of the financial instruments, Grimm plc (Grimm) has the...

Grimm plc (Grimm) has the following transactions: a) On 1 st January 2010, Grimm issued 400,000 convertible £1 6% debentures for £600,000.  The professional fees associated wit

#According to the CDC there were 597, Ask question #Minimum 100 words acceA...

Ask question #Minimum 100 words acceAccording to the CDC there were 597,689 deaths in the US in 2010 attributed to heart disease. a) Given That the US population in 2010 was clos

Define markov chain, Define Markov chain Random processes with Markov ...

Define Markov chain Random processes with Markov property which takes separate values, whether t is discrete or continuous, are known as Markov chains.

Diferential equations, Find the normalized differential equation which has ...

Find the normalized differential equation which has {x, xex} as its fundamental set

probability , An engineer has 200 resistors that he keeps in one box. Resi...

An engineer has 200 resistors that he keeps in one box. Resistors are colored to help their identification, and in this box there are 30 white resistors, 50 black resistors, 80 red

Determine does this point lie on the line, Does this Point Lie on The Line?...

Does this Point Lie on The Line? How do you know if a point lies on a given line? For example, does the point (1, 2) lie on the line 3x + y = 7? If you graph the line and the

What is the total number of pounds they bought if the total, The student co...

The student council bought two various kinds of candy for the school fair. They purchased 40 pounds of candy at $2.15 per pound and x pounds at $1.90 per pound. What is the total n

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