Linear approximations, Mathematics

Assignment Help:

Linear Approximations

In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to take derivatives, thus in some way this is an application of derivatives as well.

Given a function, f ( x ) , we can determine its tangent at x = a .  The equation of the tangent line, that we'll call L ( x ) for this discussion, is,

                            L ( x ) = f ( a ) + f ′ ( a ) ( x - a )

 Take a look at the given graph of a function & its tangent line.

2178_l hospital limit.png

From the graph we can illustrates that near x = a the tangent line & the function have closely the similar graph.  On instance we will utilizes the tangent line, L ( x ) , as an approximation to the function, f ( x ) , near x = a .  In these cases we call the tangent line the linear approximation to the function at x = a .


Related Discussions:- Linear approximations

What is terminology of quadratic functions, What is Terminology of Quadrati...

What is Terminology of Quadratic Functions ? The function in x given by: F(x) = ax 2 + bx + c, where a 0 is called a quadratic function. The graph of a quadratic function is

Rejection and acceptance regions, Rejection and Acceptance regions All ...

Rejection and Acceptance regions All possible values which a test statistic may either suppose consistency along with the null hypothesis as acceptance region or lead to the re

Permutations and combinations, How many arrangements can be made from the l...

How many arrangements can be made from the letters of the word " VENUS " such that the order of the vowels remains the same?

Describe least three characteristics at medieval world, Based upon the prim...

Based upon the primary sources, describe at least three characteristics that mark the early modern world as distinctly different than the Medieval world that preceded it. You might

Complex number, a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.fi...

a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k

Working definition of limit - sequences and series, Working Definition of L...

Working Definition of Limit 1. We state that if we can create an as close to L like we want for all adequately large n.  Alternatively, the value of the a n 's approach

Fractions, what is the lowest term of 11/121

what is the lowest term of 11/121

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