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

Find the are length and sketch the level curves, 1) Find the are length of ...

1) Find the are length of r(t) = ( 1/2t^2, 1/3t^3, 1/3t^3) where t is between 1 and 3 (greater than or equal less than or equal) 2) Sketch the level curves of f(x,y) = x^2-2y^2

Lengrange''s mean value theorem, real life applications of lengrange''s mea...

real life applications of lengrange''s mean value theorem

Precalculus, how does sin of x equal negative 1/3

how does sin of x equal negative 1/3

Euler equations with an auxiliarty condition - shortest path, 1. Finding th...

1. Finding the shortest path btween any two points on the surface of a sphere but use the method of the euler equations with an auxiliarty condition imposed? Question2:

Conduct an appropriate hypothesis test, Aspire LLP is a recruitment agency....

Aspire LLP is a recruitment agency. Recently, the company senior manager, Kay conducted a survey to understand the number of hours students spend daily on their studies after schoo

Find out the dimensions of the field-optimization, We have to enclose a fie...

We have to enclose a field along with a fence. We contain 500 feet of fencing material & a building is on one side of the field & thus won't require any fencing.  Find out the dime

Rebecca is 12.5% taller than debbie how tall is rebecca, Rebecca is 12.5% t...

Rebecca is 12.5% taller than Debbie. Debbie is 64 inches tall. How tall is Rebecca? Because Rebecca is 12.5% taller than Debbie, she is 112.5% of Debbie's height (100% + 12.5%

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