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

Density Determination, If the mass is 152.2g and the volume is 18cm3, then ...

If the mass is 152.2g and the volume is 18cm3, then what is the density?

External forces, It is the catch all force. If there are some other forces ...

It is the catch all force. If there are some other forces which we decide we need to act on our object we lump them in now and call this good. We classically call F(t) the forcing

String art, finding distance using circumference

finding distance using circumference

Example of probability, Example of Probability: Example: By using...

Example of Probability: Example: By using a die, what is the probability of rolling two 3s in a row? Solution: From the previous example, there is a 1/6 chance of

Leptokurtic-measure of central tendency, Leptokurtic a) A frequency di...

Leptokurtic a) A frequency distribution which is lepkurtic has normally a higher peak than that of the general distribution. The coefficient of kurtosis while determined will

Estimate how much should every friend pay, A group of ?ve friends gone out ...

A group of ?ve friends gone out to lunch. The total bill for the lunch was $53.75. Their meals all cost about the similar, so they needed to split the bill evenly. Without consider

Mean is 8.32 find the median, In a frequency distribution mode is 7.88, mea...

In a frequency distribution mode is 7.88, mean is 8.32 find the median.  (Ans: 8.17) Ans:  Mode = 3 median - 2 mean 7.88 = 3 median - 2 x 8.32 7.88 +16.64 = 3 median

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