Hans Lundmark
Reputation
23,272
Top tag
Next privilege 25,000 Rep.
Access to site analytics
Badges
4 45 82
Newest
Impact
~850k people reached

• 14 helpful flags
• 8,579 votes cast

# 2,915 Actions

 8h answered Why do a distance and its square reach their minimum at the same point? 9h comment How can I evaluate the limit of this function using series? Did you cancel $x^2$ from the numerator and the denominator? 15h comment Compute $\lim_{t\to0}\frac{f(2+t,3+t)-f(2,3)}{t}$ using the partial derivatives of $f$ Don't bother about adding and subtracting $f(2+t,3)$, since you can't use the definition of partials directly anyway. Just apply the definition of differentiability to the original expression. 23h comment Compute $\lim_{t\to0}\frac{f(2+t,3+t)-f(2,3)}{t}$ using the partial derivatives of $f$ Just from the existence of partial derivatives you cannot prove anything about your limit; you'll need to assume that $f$ is differentiable, and then use the definition of differentiability. 1d comment Extending the Riemann integral to any compact set See en.wikipedia.org/wiki/Smith%E2%80%93Volterra%E2%80%93Cantor_set for an example of a compact set whose boundary (equal to the set itself) has positive measure. 1d comment Are there theoretical applications of trigonometry? See also here: math.stackexchange.com/questions/8337/… 1d comment Alternating sum of combinations of the n by consecutive k An easier method for this particular case (but not as general): expand $(1+(−1))^n$. Apr 28 comment What book about algebraic combinatorics is it? @boumol: As I interpret it, they are a work in progress (and hence not published yet). Apr 28 answered What book about algebraic combinatorics is it? Apr 27 answered Understanding the proof of catalan numbers using lattice paths Apr 27 comment The determinant of adjugate matrix @user124697: math.stackexchange.com/questions/881654/… Apr 25 comment Why some of the value in inverse matrix become positive? Then follow this link: bancomicsans.com/main ;-) Apr 25 comment Geometrical Interpretation of Tensors (intuition) Did you look at this question (asked by a physics student): math.stackexchange.com/questions/10282/…? Apr 24 answered Show that $\dfrac{\rm{d}^{L-m}}{\rm{d}x^{L-m}}\left(x^2-1\right)^L=\dfrac{(L-m)!}{(L+m)!}(x^2-1)^m\dfrac{\rm{d}^{L+m}}{\rm{d}x^{L+m}}(x^2-1)^L$ Apr 23 revised Hirota's Bilinear Form edited tags Apr 22 awarded Nice Answer Apr 22 comment About the definition of isolated singularity of a complex function For the definition of isolated singularity, it doesn't matter whether $f(a)$ is defined or not. It's a removable singularity if you can define $f(a)$ (or redefine, if $f(a)$ already was defined but with an “incorrect” value) so that $f$ becomes analytic in $B(a;R)$. Apr 22 comment About the definition of isolated singularity of a complex function Second edition. Interesting that even he managed to get it wrong in the first edition. Nobody's perfect! Apr 22 comment What is the Taylor series expansion of $z^{1/2}$ about origin. The polar form of the CR equations is only valid for $r>0$. (Polar coordinates are singular at the origin, since the angle is undefined there.) Apr 22 comment The function such that $\ln(e^z)=z$? That would be difficult, since the exponential function isn't injective on $\mathbb{C}$...