integral of 1/x

This is a discussion on integral of 1/x within the A Brief History of Cprogramming.com forums, part of the Community Boards category; can you take the derivative using the log of any base and not just ln? i'm reading about 'logarithmic differentiation' ...

  1. #16
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    can you take the derivative using the log of any base and not just ln? i'm reading about 'logarithmic differentiation' and so far I only have yet to see them taking the natural log of both sides of the equation to solve for the derivative of some function

  2. #17
    ¡Amo fútbol!
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    Yep, you can. When you take the derivative, there will be a ln 10 on both sides which cancel out through division.

  3. #18
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    do any of you guys know of the scientific way to compute the logarithm of a number. I want to program my own natural logarithm function, just for the heck of it, which I guess I could then in turn use for any other base by using change of base formulas.

  4. #19
    'AlHamdulillah
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    from mathforum.org:


    ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + ...(repeating to infinity)
    mathforum

  5. #20
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    sweet dude thanks

  6. #21
    'AlHamdulillah
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    no problem, I started calculus I this semester, but have read a head a bit, so I knew alittle bit more what to look for(for instance, I knew to look for stuff with infinite series).

  7. #22
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    that's pretty cool. we might be on the same level, where exactly are you at? I'm in chapter 7 of our book, which is about half way (we're starting integrals). If we're at exactly the same spot we might be able to volley questions back and forth when we are doing homework and stuck. I really like calculus I'm getting a retardedly high grade in it and I *think* I understand everything at an intuitive level. want to read my latest portfolio? it's about the fundamental theorem of calculus explaining why and how integrals work...sweet stuff d00d!!!!!!!!!!!

  8. #23
    'AlHamdulillah
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    Well, we have just gotten past the part in our covering derivatives, and all of the shortcuts to differentiation and we now are working on the application side of derivatives, we touch integrals in a little bit though.

    I am ........ed off at myself though right now, I think botched a test I should of aced because of a stupid stomach bug that I got at the same time as one of those "my head is so cloudy I can barely think" cold bugs(also, I attributed a principle of a derivative of a function to the function itself, the " there is no derivative at a point, if the point is a sharp corner of the function" property of derivatives... I attributed it to continuous functions in general....(another reason why poor sleeping habits suck in college).

    It is great fun though, what is your text book, by any chance? and can you give me a basic overview of what you have covered so far?.

    EDIT: In case your wondering about how well I do in calculus, besides messing up on the test, I have a score of 99% in the class.
    Last edited by EvBladeRunnervE; 03-17-2004 at 04:10 PM.

  9. #24
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    are you talking about a function such as:

    y = abs(x)

    where x is zero and has no derivative?

    My book is called "Calculus: Algebraic and Numerical"...I don't remember off hand I can get the exact name and authors.

    We've covered all of the basic calc stuff (limits and continuity and derivatives). The hardest stuff we've done was related rates. that's the same score i got first semester!

  10. #25
    'AlHamdulillah
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    wait a sec, your second semester in calculus?


    where x is zero and has no derivative?
    yeah, y = abs(x) is the type of function I am talking about. I really dislike messing up on tests(hell, I get royally ........ed if I score below 95 on anything scientific).

  11. #26
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    ya but my class is really slow...we're collectively retarded, im the only one who 'gets' any of it. I said i'm in chapter 7, but the class is in chapter 5. Were *just* starting integrals, so I'm sure you and I are pretty damn close to being at the same level.

  12. #27
    'AlHamdulillah
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    Yeah, the class goes pretty slow for me to, I am planning on reading ahead and getting done with all the calc 2 stuff during the summer(single variable integration, the whole works). I honestly dont understand why people have the collective stupidity when it comes to derivatives, what is so hard to understand about instantaneous rate-of-change? Alot of people in my class have problems with the shortcuts to differentiation, because they never tried solving for it using the old limit as h -> 0 of (f(x+h) - f(x))/h , well, it is because they dont know how to generalize things, for example, the chain rule can be generalized fromthe derivative of e^(u(x)).

  13. #28
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    no no no using that is the worst way to teach the chain rule...the chain rule is the easiest and simplest calculus idea ever so you shouldn't obfusc it by trying to use e^u caca

  14. #29
    'AlHamdulillah
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    I know it is simple, however, noone really tries to figure it out by themselves the hardest way possible(i.e. the way that usually you will get the most from it if you understand it at all).

    EDIT: Sort of like finding the derivative of sin x. you get to a point where it is : sin x lim [(cos h - 1)/h] + cos x lim (sin h)/h. We know the limit of sin h / h is 1 and the limit of cos h -1 / h is 0.
    Last edited by EvBladeRunnervE; 03-17-2004 at 05:23 PM.

  15. #30
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    Why would you want to figure out the chain rule the hardest way possible? It's the easiest thing to get an intuitive understanding of. I can't remember how to derive the sandwich rule or the trig identities unfortunately
    Ill have to read up on that again

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