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

Steps for radio test - sequences and series, Steps for Radio test Assum...

Steps for Radio test Assume we have the series ∑a n Define, Then, a. If L b. If L>1 the series is divergent. c. If L = 1 the series might be divergent, this i

Find final position of point by rotation -translation matric, Question: ...

Question: A point in 3D is first rotated anticlockwise by 45 degrees about x axis,then translated along y axis by 2 units.Find the final position of the point if its initial po

Initial condition for differential equations, Initial Condition(s) are a se...

Initial Condition(s) are a set of conditions, or a condition on the solution which will permit us to find out that solution which we are after.  Initial conditions are frequently a

Sas, can you tell me how to find the "x" and the "y" when trying to find if...

can you tell me how to find the "x" and the "y" when trying to find if two triangles are smiliar

Definition of natural exponential function, Definition of Natural exponenti...

Definition of Natural exponential function:   The natural exponential function is f( x ) = e x   where, e= 2.71828182845905........ . Hence, since e > 1 we also know that e x

Advanced functions, writ the equation that describes the motion of a point ...

writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a

prove that x = 2h/3, A vertical post stands on a horizontal plane.  The an...

A vertical post stands on a horizontal plane.  The angle of elevation of the top is 60 o and that of a point x metre be the height of the post, then prove that x = 2 h/3 .

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

Derive the hicksian demand function using indirect utility , (a) Derive the...

(a) Derive the Marshalian demand functions and the indirect utility function for the following utility function: u(x1, x2, x3) = x1 1/6 x2 1/6 x3 1/6    x1≥ 0, x2≥0,x3≥ 0

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