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  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...
  16. FilupSmith

    Please help me understand gravity.

    Its true that it isn't a sound analogy, but It does show the same outcome, does it not?
  17. FilupSmith

    Please help me understand gravity.

    Ah, thank you for that! My mistake aha. You are right, gravity is the effect caused by the curvature of space time just like how the speed at which the tennis ball moves towards the bowling ball if due to the curvature of the trampoline!
  18. 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...
  19. FilupSmith

    Please help me understand gravity.

    As you mentioned, gravity effects spacetime - just as a bowling ball does on a trampoline. What you wanted to know is about gravity having speed - what i want to correct is that gravity doesnt have a 'speed' as such. Gravity is an attraction - like a magnet. Magnets do not have a speed, but they...
  20. FilupSmith

    Why doesn't air form shadows?

    Just like the post above, but I'd like to add a few more details. Have you ever looked at your shadow when it bright and sunny? Move your hand further away from the ground... what will happen is that the shadow will look blurry. Why? As the above stated, diffraction comes into effect BUT more...
  21. 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...
  22. FilupSmith

    Definite integral

    Having a positive or negative area indicates its direction above or below the axis. For example: $$ \int^{1}_{0}-x^{2}dx=\left[-\dfrac{1}{3}x^{3}\right]^{1}_{0} $$ ##= -\dfrac{1}{3} ## This indicates, that between x=0 and x=1 for x2, there is a 1/3 area2 DOWNWARDS (below the x-axis in...
  23. FilupSmith

    Download the free PF App for iPhone/Android phones!

    I can't wait! Also, because I primarily use my phone, is there a way or forum I can use to learn LaTeX? ~| FilupSmith |~
  24. FilupSmith

    Finding area given definite integral

    I'm pretty sure the this is what you're looking for: $$ \int ^{b}_{a}2xdx=\left[ x^{2}\right] ^{b}_{a}=b^{2}-a^{2} $$ ~| FilupSmith |~
  25. FilupSmith

    Finding area given definite integral

    Hope this helps ∫ba 2s ds = [s2]ba this then becomes (b2-a2) its just integral laws
  26. FilupSmith

    Question about the exponential growth and decay formula

    That helps a lot! Thanks! ~| FilupSmith |~
  27. FilupSmith

    Question about the exponential growth and decay formula

    I thought so, I initially noticed this when solving for t. Because e kind of disappears once you take the natural log. I guess its really for convenience? None the less, thank you very much! ~| FilupSmith |~
  28. FilupSmith

    Download the free PF App for iPhone/Android phones!

    Why doesn't the phone allow for LaTeX view in app? It's kinda frustrating. ~| FilupSmith |~
  29. 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 |~
  30. FilupSmith

    Why Does cos(180-Θ) = -cos(Θ)?

    What you have to remember is that when you draw your unit circle, you need to remember ASTC. The region which 180-θ falls in is the second quadrant — or, the S quadrant. In this quadrant, only sin is positive. So cos(180-θ)=-cosθ Hope this helps ~| FilupSmith |~
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