The limit, Mathematics

Assignment Help:

The Limit : In the earlier section we looked at some problems & in both problems we had a function (slope in the tangent problem case & average rate of change in the rate of change problem) and we desired to know how that function was behaving at some point x = a .  At this stage of the game we no longer care where the functions came from & we no longer care if we're going to illustrates them down the road again or not. All that we have to know or worry regarding is that we've got these functions and we desire to know something about them.

To answer the questions in the last section we select values of x that got closer & closer to

x = a and we plugged these in the function.  We also ensured that we looked at values of x that were on both the left & the right of x = a .  one time we did it we looked at our table of function values & saw what the function values were approaching as x got closer & closer to x = a and utilized it to guess the value that we were after.

This procedure is called taking a limit and we have some notation for this. For instance the limit notation is,

561_limit.png

In this notation we will consider that we always give the function which we're working with and we also give the value of x (or t) that we are moving in towards.

In this section we will take an intuitive approach to limits & try to obtain a feel for what they are and what they can tell us concerning a function. Along with that goal in mind we are not going to get into how we in fact compute limits yet.

Both of the approaches that we are going to use in this section are designed to help us understand just what limits are.  In general we don't typically use the methods in this section to compute limits and in several cases can be very hard to use to even estimate the value of a limit and/or will give the wrong value on occasion.  We will look at actually computing limits in a couple of sections.


Related Discussions:- The limit

Determine the probability - mean and standard deviation, The scores of stud...

The scores of students taking the ACT college entrance examination are normally distributed with a mean m = 20.1 and a standard deviation s = 5.8. A single student is selected a

Application of interpolation and extrapolation, Application Interpolati...

Application Interpolation and extrapolation are widely used by businessmen, administrators, sociologists, economists and financial analysts. While interpolation hel

Evaluate the measure of the smallest angle, The calculation of the angles o...

The calculation of the angles of a triangle are shown by 2x + 15, x + 20 and 3x + 25. Evaluate the measure of the smallest angle within the triangle. a. 40° b. 85° c. 25°

Laplace transforms, Here is not too much to this section. We're here going ...

Here is not too much to this section. We're here going to work an illustration to exemplify how Laplace transforms can be used to solve systems of differential equations. Illus

Find the value of x of eagle , A fox and an eagle lived at the top of a cli...

A fox and an eagle lived at the top of a cliff of height 6m, whose base was at a distance of 10m from a point A on the ground. The fox descends the cliff and went straight to the p

Distinct eigenvalues-sketching the phase portrait, Sketch the phase portrai...

Sketch the phase portrait for the given system. Solution : From the last illustration we know that the eigenvectors and eigenvalues for this system are, This tu

Triple integrals, Consider a circular disc of radius 1 and thickness 1 whic...

Consider a circular disc of radius 1 and thickness 1 which has a uniform density 10 ?(x, y, z) = 1. (a) Find the moment of inertia of this disc about its central axis (that is, the

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