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Jul
31
comment Asymptotic direction
just an fyi: the second derivative doesn't live in the tangent space or bundle
Jul
31
comment Proof that the Runge Phenomenon occurs
the reason is given right here
Jul
31
comment Dedekind Construction Of Real Numbers
"in this topology" -- you mean the product topology on $\mathbb R^2$?
Jul
31
revised Trying to understand why 2 times the sum of consecutive integers from 0 to n is equal to n times n+1
edited body
Jul
31
answered Trying to understand why 2 times the sum of consecutive integers from 0 to n is equal to n times n+1
Jul
31
answered Quadratic equation with several variables
Jul
31
comment Reciprocals of theta functions
Weierstrass elliptic functions have second-order poles on a lattice generated by $\omega_1,\omega_2$
Jul
31
answered incremental computation of standard deviation
Jul
31
comment why does the reduced row echelon form have the same null space as the original matrix?
@beginner left multiplication of elementary matrices does not preserve the column space; right multiplication, however, does -- though then this does not preserve the null space.
Jul
31
answered Basis of a product vector space
Jul
31
answered why does the reduced row echelon form have the same null space as the original matrix?
Jul
30
comment Logic and set theory textbook for high school
I was taught from those books in middle school :)
Jul
30
comment How many $0$s does the number $30!$ have?
you only need to count the number of $5$s, as there are more than enough $2$s; regardless, this only counts trailing zeros, and misses those in the interior.
Jul
22
comment Question Regarding Cardano's Formula
@Donkey_2009 you mean Lagrange resolvents :-)
Jul
20
comment If $ \sum_{n=1}^{\infty}x_na_n $ converges when $x_n\to 0,$ then $ \sum_{n=1}^{\infty}a_n $ also converges.
read the comments on the initial post; the statement is that it should work for any $x_n\to 0$
Jul
18
comment Compute the total derivative
the total derivative is just dual to the gradient; $$df_{(x,y)}(\delta x,\delta y)=\delta x\cdot\left(\frac{\partial f}{\partial x}\right)(x,y)\,+\delta y\cdot\left(\frac{\partial f}{\partial y}\right)(x,y)\,\delta y$$
Jul
17
answered Differentials of Multivariable Functions
Jul
17
comment Differentials of Multivariable Functions
do you know the formulas for the volume and surface area of a cylinder with circular top and bottom? $2\pi rh$ gives the lateral surface area and $2\pi r^2$ the area of the top and bottom, while $\pi r^2 h$ gives the volume.
Jul
15
comment Why do we say “radius” of convergence?
if $a_n\sim r^n$ for $|r|\ge 1$ as $n\to\infty$ then we need $0\le|x-a|< 1/r=R$, so it's symmetric about $x=a$. functions for which $a_n\to0$ faster than any $r^n$ are entire
Jul
15
revised Finding a Solution to a Equation that Ends up as a Weird Repeating Series
added 2 characters in body