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

Continuity requirement, Continuity requirement : Let's discuss the continu...

Continuity requirement : Let's discuss the continuity requirement a little. Nowhere in the above description did the continuity requirement clearly come into play.  We need that t

Explain pie charts, Explain Pie Charts ? If the frequencies are writte...

Explain Pie Charts ? If the frequencies are written as percentages, they can be easily compared using a pie chart. The following is an example of a pie chart using the data fr

Complex Numbers, How do you compute the phase/angle of a complex number? i....

How do you compute the phase/angle of a complex number? i.e 1+2i

Pythagorean theorem, How do you find the perimeter of an irregular shape us...

How do you find the perimeter of an irregular shape using Pythagorean theorem?

In the terms of x, The length of Kara's rectangular patio can be expressed ...

The length of Kara's rectangular patio can be expressed as 2x - 1 and the width can be expressed as x + 6. In the terms of x, what is the area of her patio? Since the area of a

Polya’s first and second principle:-mathematical problem, Mathematical Prob...

Mathematical Problem Solving In 1945, mathematician George Polya (1887-1985) published a book titled How To Solve It in which he demonstrated his approach to solving problems.

Ratio math help, Mr.Tanaka has 56 students in his choir the ratio of boys ...

Mr.Tanaka has 56 students in his choir the ratio of boys to girls is 3:4 how many boys and girls are in his class

Classification-developing pre-number concepts, Classification :  As you kn...

Classification :  As you know, classification (also called grouping) involves putting together things that have some characteristic in common. We can say that a child is able to c

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