Recent content by FilupSmith

  1. FilupSmith

    Can you derive e^x by first principles?

    Awesome. Thanks! This is so interesting!
  2. FilupSmith

    Can you derive e^x by first principles?

    Thank you guys. Your explanations were all very informative!
  3. FilupSmith

    Help with Einstein and Planck's Views Question

    I will. Thank you ~| FilupSmith |~
  4. 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...
  5. FilupSmith

    Horse race:tilting the possibility

    Ok. I wasn't sure. Thanks :) ~| FilupSmith |~
  6. FilupSmith

    Displacement of a particle

    I know what it looks like, I'm just curious about what the displacement would be for non-real x values - but it seems to be that for ##x=f\left( t\right)##, x cannot be complex. ~| FilupSmith |~
  7. FilupSmith

    Displacement of a particle

    Ah, I see. ~| FilupSmith |~
  8. FilupSmith

    Displacement of a particle

    That sounds most probable. So for the case of ##x=\sqrt{t-2}##, ##x\in \mathbb{R}## ? ~| FilupSmith |~
  9. 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...
  10. FilupSmith

    Can you derive e^x by first principles?

    Thank you very much! And I will be sure to remember that ;) ~| FilupSmith |~
  11. FilupSmith

    Can you derive e^x by first principles?

    Oh, ok. Thanks :) ~| FilupSmith |~
  12. FilupSmith

    Can you derive e^x by first principles?

    I am referring to e=2.71828... ~| FilupSmith |~
  13. FilupSmith

    LaTeX Question about LaTeX

    I looked it up and i believe the only difference is that \tfrac or \frac allow for text sized fractions (great for 1/3, etc.) while \dfrac is best for formulas! Thanks none the less!
  14. FilupSmith

    Please help me understand gravity.

    I see... well, I'll keep that in mind. Thanks
  15. 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...
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