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Mar
12
comment Evaluate each of the numeric expressions: $\sqrt{(-3)}$, $\sqrt{3}$, $\sqrt{-3}$
As far as I know, while the equation $x^2 = a$ has two solutions for $a > 0$, $\sqrt{a}$ is defined as the positive square root, not both. This only applies when working in $\mathbb{R}$, since in $\mathbb{C}$ you can't distinguish positive and negative.
Mar
10
comment How to find average rate of change
I don't think it's so straightforward, though, since he was given the velocity, not the position (not to mention it should be a function of $t$ and not of $x$).
Mar
10
comment A proof in Spivak on integration.
@sizz: Suppose you know that $|x-y| \lt \epsilon$ for all $\epsilon > 0$. If $x \ne y$, you can take $\epsilon = |x-y|$ (because $x-y$ is not $0$), and you get $|x-y| < |x-y|$, a contradiction which came from assuming $x \ne y$.
Mar
10
answered About vector addition
Mar
8
comment Can the following equation be solved for the unknowns?
But it doesn't say through the curve, it says through the point.
Mar
8
answered Partial Derivative of $f(x,y) =\ln(x^{2} + y^{2}) + \sqrt{x^{2}\cdot y^{3}}$
Mar
8
comment Partial Derivative of $f(x,y) =\ln(x^{2} + y^{2}) + \sqrt{x^{2}\cdot y^{3}}$
$\frac{x}{\sqrt{x^2}} \ne 1$.
Mar
8
comment Can the following equation be solved for the unknowns?
How did you get that $f''(-2) = 0$? The question doesn't say anything like that.
Mar
8
comment domain of trigonometric function with greatest integer
The domain of $\sin x$ is $\mathbb{R}$.
Mar
8
comment How do I obtain the derivative of $\frac{x^2}{x-y}$?
Derivative with respect to what?
Mar
7
comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
I've always thought that it's kinda cheating to teach this to someone who doesn't fully understand complex numbers. I remember I first heard about this when I was about 16, and I thought it was some miraculous numerical coincidence, when in reality this exponentiation doesn't work like the one you know, so this identity does not mean what you think it means at that age.
Mar
6
comment Determinants and Matrices
@EngGenie: $2^8$ is $256$.
Mar
5
comment What does it mean for a sequence to be decreasing in regards to the Integral Test for Convergence?
A sequence $a_n$ is decreasing if $a_{n+1} \le a_n$ for all $n$.
Mar
4
revised Simple Calculus question about integrating a function
added 1212 characters in body
Mar
4
comment Simple Calculus question about integrating a function
I'll do some editing.
Mar
4
answered Simple Calculus question about integrating a function
Mar
4
comment Simple Calculus question about integrating a function
I'm sorry, but that's not really clearer. What does it mean for a plane to be the ordinate of $f$?
Mar
4
comment Simple Calculus question about integrating a function
I believe that $f$ is supposed to be rotated about the line $x=\frac{b-a}{2}, z=0$ (it's probably supposed to be $\frac{a+b}{2}), projected onto the $xy$ plane, and then integrated. So it will still be a function, it will be like a compressed version of $f$.
Mar
4
comment Simple Calculus question about integrating a function
I think I understand now. You mean project the rotated graph of $f$ onto the $xy$ plane, and then integrate this new function?
Mar
4
comment Simple Calculus question about integrating a function
But how do you define $F$ in terms of $\theta$? How do you integrate a rotated function? Maybe a picture would help.