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Sep
21
comment Question about solving 2nd order linear differential equations
What book are you using, by the way?
Sep
21
comment Question about solving 2nd order linear differential equations
@Korgan: If it turns out you were right, please tell us, because this is the method I've seen in every differential equations book there is. I'd be very surprised if it was wrong.
Sep
20
comment Showing vectors span a vector space by definition
This indeed uses only the defintion. I'll edit to make it more explicit.
Aug
23
comment A question on Taylor Series and polynomial
I think the OP means that the Taylor series is finite.
Aug
21
comment Graph $f(x)=\ln x+2$
@AustinBroussard: Yes, that's right.
Aug
21
comment Graph $f(x)=\ln x+2$
@AustinBroussard: I don't understand what you said about a horizontal asymptote having to do with $y \to \pm \infty$. A function has a horizontal asymptote, more or less, if it has a limit (not infinity) when $x$ goes to $\pm \infty$, and the logarithm doesn't have one. It simply goes to infinity.
Aug
21
comment Graph $f(x)=\ln x+2$
@AustinBroussard: This is a minor terminology thing. Rather than undefined, I would say that there is no y-intercept. The functions $\ln x$ and $\ln x + 2$ are undefined at $x=0$, so there is no y-intercept.
Aug
21
comment Graph $f(x)=\ln x+2$
Don't you mean $\ln x + 2$, or maybe $\ln(2+x)$?
Aug
13
comment Why can't $\int_0^1\sin(x^2) dx$ be equal to $2$?
Forgive me if I'm missing something, but why would it be 2? I mean, with so many numbers to choose from, why would you expect it to be 2?
Aug
6
comment Projectile Motion
@ladaghini: Nothing, my mistake.
Aug
6
comment Projectile Motion
@GorillaOne: Yes, sorry, I messed that up. I'll write an answer if I figure it out.
Aug
6
comment Projectile Motion
@GorillaOne: If you know those, you can find out the time from $x=x_0+v_x t$
Aug
1
comment Derivative of $x^x$ at $x=1$ from first principles
@user758556: I guess to use L'Hôpital's you would have to know $\frac{\mathrm{d}}{\mathrm{d}h} (x+h)^h$, which sorts of defeats the purpose of using the limit definition in the first place.
Jul
25
comment Having trouble understanding proof of a theorem involving limits of functions and sequences
Oh, I get it now. I'm not sure if the argument I'm thinking of is the same one the author is describing, but whatever. Your answer sure helped, though!
Jul
25
comment Why are $\sin$ and $\cos$ (and perhaps $\tan$) “more important” than their reciprocals?
Fun fact: In some languages, in particular Spanish, sine still has the same not safe for work meaning. This has lead to uncountable repressed giggles in high school math class.
Jul
22
comment Compute integral $\int_{-6}^6 \! \frac{(4e^{2x} + 2)^2}{e^{2x}} \, \mathrm{d} x$
@Matt: Isn't it simpler to just say $\mathrm{d}u = e^x\ \mathrm{d}x = u\ \mathrm{d}x \implies \frac{\mathrm{d}u}{u} = \mathrm{d}x$?
Jul
21
comment Compute integral $\int_{-6}^6 \! \frac{(4e^{2x} + 2)^2}{e^{2x}} \, \mathrm{d} x$
After doing the change of variables, shouldn't it be $u^2$ instead of $e^{2u}$ in the numerator?
Jul
21
comment Motivation for definition of logarithm in Feynman's Lectures on Physics
I just saw in the feynmanlectures.info site that this has been added to the errata. Awesome!
Jul
20
comment Find all solutions, other than $2$ for $12x^3-23x^2-3x+2=0$
@Austin: You don't need to ask. You could just plug in those values and check whether they satisfy your equation.
Jul
19
comment Help solving differential equation: $y' = x\sqrt{4+y^{2}}/{y(9+x^{2})}$
The right side of the equality can be written as $\frac{\sqrt{4+y^2}}{y} \frac{x}{(9+x^2)}$. Does this help?