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

Law of Cosines, The law of cosines can only be applied to acute triangles. ...

The law of cosines can only be applied to acute triangles. Is this true or false?

Reason for why limits not existing, Reason for why limits not existing : I...

Reason for why limits not existing : In the previous section we saw two limits that did not.  We saw that did not exist since the function did not settle down to a sing

Differentiate the equation x = x (t ) and y = y (t ) , Suppose that x = x (...

Suppose that x = x (t ) and y = y (t ) and differentiate the following equation with respect to t. Solution                                         x 3 y 6 + e 1- x - cos (5

Prime number, Prime number A prime number is a number whose only +ve fa...

Prime number A prime number is a number whose only +ve factors are 1 and itself. For instance 2, 3, 5, and 7 are all of the examples of prime numbers.  Examples of numbers whic

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Geometry, prove angle MJL is congruent to angle KNL

prove angle MJL is congruent to angle KNL

Stats, the automatic hopper loader is set to put 36 tons of coal in each ca...

the automatic hopper loader is set to put 36 tons of coal in each car. the actual weights of coal loaded into each car arw normally distributed with a mean of 36 tons and a standar

Nonhomogeneous systems, We now require addressing nonhomogeneous systems in...

We now require addressing nonhomogeneous systems in brief. Both of the methods which we looked at back in the second order differential equations section can also be used now.  Sin

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