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

Krystal, what is the tenths place

what is the tenths place

Write following in terms of simpler logarithms, Write following in terms of...

Write following in terms of simpler logarithms.  (a) log 3 (9 x 4    / √y) Solution log 3 (9 x 4 / √y) =log ­ 3 9x 4 -  log  y (1/2) =log ­ 3 9 + log ­ 3 x 4

Detremine the surface area to the nearest inch, If a tabletop has a diamete...

If a tabletop has a diameter of 42 in, Detremine the surface area to the nearest inch? (π = 3.14) a. 1,384 in 2 b. 1,319 in 2 c. 1,385 in 2 d. 5,539 in 2 c. Th

Solving whole number riddles, What is the answer for I am greater than 30 a...

What is the answer for I am greater than 30 and less than 40. The sum of my digits is less than 5.

Melisa and jennifer threw a fiftieth how much is a 20% tip, Melisa and Jenn...

Melisa and Jennifer threw a fiftieth birthday party for their father at a local restaurant. While the bill came, Melisa added a 15% tip of $42. Jennifer said in which the service w

Correlation, How o make vicariate frequency distribution table

How o make vicariate frequency distribution table

Opt math, howwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww...

howwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

Find and classify all the equilibrium solutions, Find and classify all the ...

Find and classify all the equilibrium solutions to the subsequent differential equation. y' = y 2 - y - 6 Solution First, get the equilibrium solutions. It is generally

What percentage of the soda purchased was cola, 3/5 of the soda purchased a...

3/5 of the soda purchased at the football game was cola. What percentage of the soda purchased was cola? Change the fraction to a decimal through dividing the numerator through

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