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Mathematics 45 Online
OpenStudy (anonymous):

The natural logarithm The natural logarithm (ln x) can be approximated with the following series: ln x = lna + (x − a) a − (x − a)2 2a2 + (x − a)3 3a3 − +· · · , 0 < x ≤ 2a Visualize this approximation of ln x around x = a. Write a program to calculate ln x given a specific a. Try to generate each term of the sum from the previous one. The input should be x and a as well as the number of terms for the sum. The output should be the approximate value of ln x. Compare the approximation with the value calculated by Maple.

OpenStudy (anonymous):

can some one translate what this problem is asking me to do ?, am having trouble understanding it.

OpenStudy (anonymous):

does it deal with summation notation?

OpenStudy (anonymous):

Yes. Basically you can approximate the natural log of a number x by the following:\[\ln x=\ln a+\frac{(x-a)}{a}-\frac{(x-a)^2}{2a^2}+\frac{(x-a)^3}{3a^3}...\]

OpenStudy (anonymous):

okay but where does that come from, that appropriation?

OpenStudy (anonymous):

are we to just take that as a given?

OpenStudy (anonymous):

In your problem you take it as a given. It comes from Taylor's Theorem, if you took Calculus it should be familiar.

OpenStudy (anonymous):

yes i thought so. So then in my problem i have to write that sum(the symbolic approximation of ln x) in summation notiation. And then write a program to calculate lnx at a speccific a

OpenStudy (anonymous):

The key step is "generate each term of the sum from the previous one"...

OpenStudy (anonymous):

can you explain a little bit more why thats the key step??

OpenStudy (anonymous):

well really all i want to know if this statment is true:So then in my problem i have to write that sum(the symbolic approximation of ln x) in summation notiation. And then write a program to calculate lnx at a speccific a?

OpenStudy (anonymous):

yeah

OpenStudy (anonymous):

wouldnt writing it in summation notation, take care of ""generate each term of the sum from the previous one".?

OpenStudy (anonymous):

yeah, pretty much

OpenStudy (anonymous):

okay, thanks eseidl!!!

OpenStudy (anonymous):

got any pseudo code for this @eseidl ?

OpenStudy (anonymous):

no problem. hope it helped.

OpenStudy (anonymous):

quick question: how do i know how many terms to generate? like in my summation notation, i am thinking something like this|dw:1347728754401:dw|

OpenStudy (anonymous):

@Algebraic! I have no experience with computer code/computer science. @crabtree34 the greater the number of terms used, the better the approximation to lnx. With infinte terms, the relation becomes exact. That being said, in any real calculate, the number of terms to use will be an input selected by the user.

OpenStudy (anonymous):

do you have an idea of home my summation notation should look:|dw:1347728964288:dw|

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