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

Evaluate following. 0ln (1+)excos(1-ex)dx substitution, Evaluate following....

Evaluate following. ∫ 0 ln (1 + π )   e x cos(1-e x )dx Solution The limits are little unusual in this case, however that will happen sometimes therefore don't get

Consumer behavior, explain big 5 ppersonality model, suggest thier target m...

explain big 5 ppersonality model, suggest thier target market and one marketing strategiy for each .

Problem solver, a bathroom measure 250 cm by 175 cm calculate the side of t...

a bathroom measure 250 cm by 175 cm calculate the side of the largest square tile that can tile the floor

Linear Programming, describe phases of operations research study ?

describe phases of operations research study ?

Christie paid 5% sales tax purchase how much did she spend, Christie purcha...

Christie purchased a scarf marked $15.50 and gloves marked $5.50. Both items were on sale for 20% off the marked price. Christie paid 5% sales tax on her purchase. How much did she

Determine the measurements of segments and angles, Determine the Measuremen...

Determine the Measurements of Segments and Angles Postulate 1.5 (The Distance Postulate) There is a unique positive number corresponding to every pair of points. Pos

Basics of series - sequences and series, Series - The Basics That top...

Series - The Basics That topic is infinite series.  So just define what is an infinite series?  Well, let's start with a sequence {a n } ∞ n=1 (note the n=1 is for convenie

Compute the measure of the larger angle, Two angles are supplementary. The ...

Two angles are supplementary. The evaluate of one is 30 more than twice the measure of the other. Determine the measure of the larger angle. a. 130° b. 20° c. 50° d. 70

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