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  1. FilupSmith

    Help with Einstein and Planck's Views Question

    Question: Outline how Einstein's and Planck's views of Science differed in relation to Science research being influenced by society an politics. I can't remember anything about this and I'm having trouble finding the information needed. Can some one please help me understand what is is that...
  2. FilupSmith

    Displacement of a particle

    A few months ago, I stumped my Mathematics teacher with a question when we were learning about displacement of a particle, given a formula. For example, ##x=t^{2}-t-1##, where x is in meters and t is in seconds. Anyway, she made it very clear how to solve displacement when given time t...
  3. FilupSmith

    Can you derive e^x by first principles?

    Differentiation by first principles is as followed: $$y'=\lim_{h\rightarrow 0}\dfrac {f\left( x+h\right) -f\left( x\right) }{h}$$ So, assuming that ##y= e^{x},## can we prove, using first principle, that: $$\dfrac{dy}{dx}\left( e^{x}\right) =e^x$$ Or is there other methods that are...
  4. FilupSmith

    Horse race:tilting the possibility

    So, today we were studying the introduction of probability. For me it is fairly simple (for now). My question is something we discussed during class today. When betting on a horse before a horse race - say, a race of 5 horses, the odds ARE NOT 1/5 because the odds are not equal (eg. one...
  5. FilupSmith

    LaTeX Question about LaTeX

    Hi, I'm trying to learn LaTeX and one of the things I'm trying to figure out is what is the difference between \frac and \dfrac? I mean, look: \frac{a}{b} is: $$\frac{a}{b}$$ \dfrac{a}{b} is: $$\dfrac{a}{b}$$ Other then the thickened line, is there really any difference? Thank you...
  6. FilupSmith

    Question about the exponential growth and decay formula

    [I don't know if this is in the right topic or not so I hope I'm all good] My question is related to the exponential growth and decay formula Q=Ae^(kt). Simply, why is the value e used as the base for the exponent? Does it have to be e? If so, can anybody tell me why? Thanks ~| FilupSmith |~