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

Zero-day attack, What is Zero-Day Attack? Explain Zero-Day Attack

What is Zero-Day Attack? Explain Zero-Day Attack

Evaluate numerator and denominator limit, Evaluate following limits. ...

Evaluate following limits. Solution : Let's do the first limit & in this case it sees like we will factor a z 3 out of the numerator and denominator both. Remember that

Describe independent events in maths, Describe Independent Events in maths?...

Describe Independent Events in maths? Events are independent if the outcome of one event does not affect the outcome of the second event. If A represents one independent event

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that each word contain 2vowles and 3consonant

Managment Science, Classify models based on the degree of their abstraction...

Classify models based on the degree of their abstraction, and provide some examples of such models.

Complex, find all the 8th roots of (19+7i)

find all the 8th roots of (19+7i)

Sums, what is 10 times 10 pls

what is 10 times 10 pls

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