# Search results

1. ### Can you derive e^x by first principles?

Awesome. Thanks! This is so interesting!
2. ### Can you derive e^x by first principles?

Thank you guys. Your explanations were all very informative!
3. ### Help with Einstein and Planck's Views Question

I will. Thank you ~| FilupSmith |~
4. ### 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. ### Horse race:tilting the possibility

Ok. I wasn't sure. Thanks :) ~| FilupSmith |~
6. ### 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. ### Displacement of a particle

Ah, I see. ~| FilupSmith |~
8. ### Displacement of a particle

That sounds most probable. So for the case of $x=\sqrt{t-2}$, $x\in \mathbb{R}$ ? ~| FilupSmith |~
9. ### 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. ### Can you derive e^x by first principles?

Thank you very much! And I will be sure to remember that ;) ~| FilupSmith |~
11. ### Can you derive e^x by first principles?

Oh, ok. Thanks :) ~| FilupSmith |~
12. ### Can you derive e^x by first principles?

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

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

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

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. ### 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...

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. ### 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. ### 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. ### 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...

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. ### 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. ### Finding area given definite integral

Hope this helps ∫ba 2s ds = [s2]ba this then becomes (b2-a2) its just integral laws
26. ### Question about the exponential growth and decay formula

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