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 angles, What is Angles? An angle is made up of two rays with a ...

What is Angles? An angle is made up of two rays with a common endpoint, which is called the vertex. The sides of the angle are rays. An angle is denoted by "θ". When two li

Midpoint rule - approximating definite integrals, Midpoint Rule - Approxima...

Midpoint Rule - Approximating Definite Integrals This is the rule which should be somewhat well-known to you. We will divide the interval [a,b] into n subintervals of equal wid

Math, what is quantity ?

what is quantity ?

Break even point, what is break even point and how can it helps managers to...

what is break even point and how can it helps managers to make decisions?

Definition of functions, Definition: An equation is considered as function...

Definition: An equation is considered as function if for any x in the domain of the equation (the domain is the entire x's which can be plugged into the equation) the equation wil

#Regular Expression, Find the Regular Grammar for the following Regular Exp...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

Solid, The lateral edge of a pyramidal church spire is 61feet.Each side of ...

The lateral edge of a pyramidal church spire is 61feet.Each side of its octagonal base is 22feet. What will be the cost of painting the spire at 2.5 cents a square foot

Illustrate Ionic solids, Ionic solids, which have anionic vacancies because...

Ionic solids, which have anionic vacancies because of metal excess defect develop colour. Illustrate with the help of a suitable example.

How much sales tax did she pay if items was 6 percent, Lindsay purchased a ...

Lindsay purchased a pocketbook for $45 and a pair of shoes for $55. The sales tax on the items was 6%. How much sales tax did she pay? Find out the price of the two items toget

What was his weight within pounds and ounces, Justin weighed 8 lb 12 oz whi...

Justin weighed 8 lb 12 oz while he was born. At his two-week check-up, he had gained 8 ounces. What was his weight within pounds and ounces? There are 16 ounces within a pound.

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