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

how many of the original vectors, We have claimed that a randomly generate...

We have claimed that a randomly generated point lies on the equator of the sphere  independent of where we pick the North Pole.  To test this claim randomly generate ten  vectors i

Two tailed tests, Two Tailed Tests A two tailed test is generally used ...

Two Tailed Tests A two tailed test is generally used in statistical work as tests of significance for illustration, if a complaint lodged by the client is about a product not m

Explain peano''s axioms with suitable example, Question 1 Explain Peano's ...

Question 1 Explain Peano's Axioms with suitable example Question 2 Let A = B = C= R, and let f: A→ B, g: B→ C be defined by f(a) = a+1 and g(b) = b 2 +1. Find a) (f °g

F distribution or variance ratio distribution, Frequency Distribution or Va...

Frequency Distribution or Variance Ratio Distribution This was developed by R. A Fisher in 1924 and is normally defined in terms of the ratio of the variances of two usually d

How to make equations of conics easier to read, How to Make Equations of Co...

How to Make Equations of Conics Easier to Read ? If you want to graph a conic sections, first you need to make the equation easy to read. For example, say you have the equatio

Find the largest clique, Generate G(1000,1/2) and find the largest clique ...

Generate G(1000,1/2) and find the largest clique you can.  A clique is a complete sub graph, that is, a set of vertices each pair of which is connected by an edge.

Algebra, 25 algebraic equations that equal 36

25 algebraic equations that equal 36

How long will it take her to save $350, Each week Jaime saves $25. How long...

Each week Jaime saves $25. How long will it take her to save $350? Divide $350 by $25; 350 ÷ 25 = 14 weeks.

AREA, How do you find the distributive property any faster?

How do you find the distributive property any faster?

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