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

Solution of triangles, In triangle ABC, if sinA/csinB+sinB/c+sinC/b=c/ab+b...

In triangle ABC, if sinA/csinB+sinB/c+sinC/b=c/ab+b/ac+a/bc then find the value of angle A.

Determination of the regression equation, Determination of the Regression E...

Determination of the Regression Equation The determination of the regression equation such given above is generally done by using a technique termed as "the method of least sq

Melisa and jennifer threw a fiftieth how much is a 20% tip, Melisa and Jenn...

Melisa and Jennifer threw a fiftieth birthday party for their father at a local restaurant. While the bill came, Melisa added a 15% tip of $42. Jennifer said in which the service w

Calculate the density of people per square mile, 1.  In 1900, a certain cou...

1.  In 1900, a certain country's population was 77,977,459 and it's area was 2,821,924 square miles, In 2000, the country's population was 283,575,229 and its area was 3,551,003 sq

Write prim's algorithm, Write Prim's Algorithm.   Ans: Prim's algorithm...

Write Prim's Algorithm.   Ans: Prim's algorithm to find out a minimum spanning tree from a weighted graph in step by step form is given below.  Let G = (V, E) be graph and S

Homotopy, prove same homotopy type is an equivalent relation

prove same homotopy type is an equivalent relation

Line plots, how to you find the difference between different line plots

how to you find the difference between different line plots

Determine the properties and query are definable in datalog, We now focus o...

We now focus on the use of Datalog for defining properties and queries m graphs. (a) Suppose that P is some property of graphs definable in Datalog. Show drat P is preserved und

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