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

Abstract algebra, How many homomorphism are there from z2 to z3. Zn is grou...

How many homomorphism are there from z2 to z3. Zn is group modulo n

Equation, how do you slove 4u-5=2u-13

how do you slove 4u-5=2u-13

Find out equation is a function, Example: Find out which of the following ...

Example: Find out which of the following equations functions are & which are not functions.                            y= 5x + 1 Solution The "working" definition of fu

Calculate the total surface area which is exposed , A golf ball has a diame...

A golf ball has a diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate the total surface area which is exposed to the surroundings assuming that the d

Slopes downward from left to right has a positive slope, Can you explain th...

Can you explain that it is true that a line that slopes downward from left to right has a positive slope?

Explain simple classification and chance and probability, E1) From your exp...

E1) From your experience, and what you have studied so far, by which age would-you expect an average child to be ready to acquire the following concepts? i) Simple classificatio

Term paper topics, please suggest me that how can i get the term papers top...

please suggest me that how can i get the term papers topics?

What is factorial, Q. What is Factorial? A factorial is a number with a...

Q. What is Factorial? A factorial is a number with a factorial sign, !, after it. 5! is read "five factorial." 3! is read "three factorial." The factorial of a natural

Estimate percent of the babies born among 6 and 8.5 pounds, 25% of babies b...

25% of babies born at Yale New Haven Hospital weigh less than 6 pounds and 78% weigh less than 8.5 pounds. What percent of the babies born at Yale New Haven Hospital weigh among 6

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