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

Ryan gym membership costs him how much is every installment, Ryan's gym mem...

Ryan's gym membership costs him $390 per year. He pays this within twelve equal installments a year. How much is every installment? To ?nd out each installment, the total yearl

Discret math, i have a question about discret math

i have a question about discret math

Calcilate the height of the cone of which the bucket , A bucket of height 8...

A bucket of height 8 cm and made up of copper sheet is in the form of frustum of right circular cone with radii of its lower and upper ends as 3 cm and 9 cm respectively. Calculate

The length of the rectangle, Suppose that the width of a rectangle is three...

Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 86 feet. a)  Set up an equation for the perimeter involving on

Probability, an insurance salesman sells policies to 5 men, all of identica...

an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p

Developing an understanidng of multiplication, DEVELOPING AN UNDERSTANIDNG ...

DEVELOPING AN UNDERSTANIDNG OF MULTIPLICATION :  The most important aspect of knowing multiplication is to understand what it means and where it is applied. It needs to be first i

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