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 annual percentage yield, 1.   Find the APY for the bank described ...

1.   Find the APY for the bank described below- A bank offers an APR of 4% compounded monthly. 2.  Use the compound interest formula to compute the balance in the following a

To find out the volume of a cube give formula, To find out the volume of a ...

To find out the volume of a cube which measures 3 cm by 3 cm by 3 cm, what formula would you use? The volume of a cube is the length of the side cubed and the length of the sid

Relations, test is tomorrow, don''t know anything lol, please help

test is tomorrow, don''t know anything lol, please help

How to converting decimals to percents, How to Converting Decimals to Perce...

How to Converting Decimals to Percents ? To convert a decimal to a percent: Move the decimal point two decimal places to the right. Place a percent sign after the resulting

Find out that vector are linearly dependent, Find out if the following set ...

Find out if the following set of vectors are linearly independent or linearly dependent. If they are linearly dependent get the relationship among them. Solution : Ther

Curve tracing, how to curve trace? and how to know whether the equation is ...

how to curve trace? and how to know whether the equation is a circle or parabola, hyperbola ellipse?

Determine the measurements of segments and angles, Determine the Measuremen...

Determine the Measurements of Segments and Angles Postulate 1.5 (The Distance Postulate) There is a unique positive number corresponding to every pair of points. Pos

Volume, Rajun uses 2/3 of a carton of milk to make a pancake. The volume of...

Rajun uses 2/3 of a carton of milk to make a pancake. The volume of milk he uses is 800ml. calculate the volume, in l, of a milk in carton?

Retail price index, Retail price index This is weighted average of pri...

Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp

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