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

2+2=5, How could 2+2 will be Equal to 5

How could 2+2 will be Equal to 5

Show that cos - cos /sin - sin = a/b, A ladder sets against a wall at an ...

A ladder sets against a wall at an angle α to the horizontal.  If the foot is pulled away from the wall through a distance of 'a', so that is slides a distance 'b' down the wall ma

Lim x, Q. lim x tends to 0 (5 tanx sinx upon x square) here ( ) this bracke...

Q. lim x tends to 0 (5 tanx sinx upon x square) here ( ) this bracket indicates greatest integer function Ans: You can calculate the limit of this function using basic concept of

How long will the board be after he makes the cut, Tom is cutting a piece o...

Tom is cutting a piece of wood to form a shelf. He cut the wood to 3.5 feet, but it is too long to fit in the bookshelf he is forming. He decides to cut 0.25 feet off the board. Ho

find the slope and the y intercept of the line - geometry, 1. Find the slo...

1. Find the slope and the y-intercept of the line whose equation is 5x + 6y = 7. 2. Find the equation of the line that is parallel to 2x + 5y = 7 and passes through the mid poin

Small samples-estimation of population mean , Estimation of population mean...

Estimation of population mean If the sample size is small (n In this case Population mean µ = x¯ ±  tS x¯  x¯ = Sample mean S x¯ =  s/√n S = standard deviation

Determine the projection - vector, Determine the Projection of b = (2, 1, -...

Determine the Projection of b = (2, 1, -1) onto a = (1, 0, -2) There is a requirement of a dot product and the magnitude of a. a →  • b → = 4                             ||a

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