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May
6
accepted Evaluate $\int_0^1 \int_\sqrt{y}^1 \int_0^{x^2+y^2} dz dx dy$.
May
6
comment Evaluate $\int_0^1 \int_\sqrt{y}^1 \int_0^{x^2+y^2} dz dx dy$.
Oh I see, so there is in fact no factor of $3$ that I am missing? The answer is indeed $26/105$?
May
5
asked Evaluate $\int_0^1 \int_\sqrt{y}^1 \int_0^{x^2+y^2} dz dx dy$.
May
1
accepted Show that $\sum_{n \neq 0} \frac{(-1)^{n+1}}{in} e^{in\theta} = 2 \sum_{n=1}^\infty (-1)^{n+1} \frac{\sin n\theta}{n}$.
May
1
asked Show that $\sum_{n \neq 0} \frac{(-1)^{n+1}}{in} e^{in\theta} = 2 \sum_{n=1}^\infty (-1)^{n+1} \frac{\sin n\theta}{n}$.
Apr
25
comment Equality in Minkowski's theorem
What is the bar notation above $g(x)$? I'm a little confused by your exposition on the first paragraph about at least one of the two functions attaining the value 0 or "pointing in the same direction". Are you assuming they are complex-valued?
Apr
23
comment Why does Fubini's theorem not hold/apply to this function?
I have that book and will take a look. Thank you.
Apr
22
accepted Why does Fubini's theorem not hold/apply to this function?
Apr
22
comment Why does Fubini's theorem not hold/apply to this function?
Is $c \times c$ in your last sentence the counting measure? Do you have any good literature on that?
Apr
22
asked Why does Fubini's theorem not hold/apply to this function?
Apr
18
accepted Let $1 \leq p <\infty$ and $f \in L^p(\mathbb{R})$. Prove $\lim_{x \to \infty} \int_x^{x+1} f(t) dt = 0$.
Apr
18
comment Let $1 \leq p <\infty$ and $f \in L^p(\mathbb{R})$. Prove $\lim_{x \to \infty} \int_x^{x+1} f(t) dt = 0$.
Is there an error in this solution? Not sure why it has a downvote as it looks correct to me.
Apr
18
asked Let $1 \leq p <\infty$ and $f \in L^p(\mathbb{R})$. Prove $\lim_{x \to \infty} \int_x^{x+1} f(t) dt = 0$.
Apr
17
asked Where is $f_x$ continuous for $f(x,y) = (x^2-y^2)/\sqrt[3]{x^2+y^2}$?
Apr
12
awarded  Popular Question
Apr
12
comment Show $(\partial^2 z / \partial x \partial y)^2 = \frac{\partial^2z}{\partial x^2} \cdot \frac{\partial^2z}{\partial y^2}$ for $z=ax + yf(a)+\phi(a)$.
Thanks for clearing up my understanding.
Apr
12
accepted Show $(\partial^2 z / \partial x \partial y)^2 = \frac{\partial^2z}{\partial x^2} \cdot \frac{\partial^2z}{\partial y^2}$ for $z=ax + yf(a)+\phi(a)$.
Apr
12
comment Show $(\partial^2 z / \partial x \partial y)^2 = \frac{\partial^2z}{\partial x^2} \cdot \frac{\partial^2z}{\partial y^2}$ for $z=ax + yf(a)+\phi(a)$.
Don't we also have that $y$ is a function of $x$ and vice versa when implicitly differentiating? (i.e. $y(x)$ so requires the product rule when differentiating $yf'(a)$?)
Apr
12
asked Show $(\partial^2 z / \partial x \partial y)^2 = \frac{\partial^2z}{\partial x^2} \cdot \frac{\partial^2z}{\partial y^2}$ for $z=ax + yf(a)+\phi(a)$.
Apr
12
accepted What is the shortest/longest distance from $9x^2 + 4y^2 = 36$ to $(5,5)$?