# Une Femme Douce

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 Sep9 accepted $\lim_{x \to 0} \left ({e^x+e^{-x}-2\over x^2} \right )^{1\over x^2}$ Sep9 comment $\lim_{x \to 0} \left ({e^x+e^{-x}-2\over x^2} \right )^{1\over x^2}$ Why the limit under log is $1$? the fraction associated with $\cosh x$ is not going to $0$ right? it is $0$ by $0$ form Sep8 asked $\lim_{x \to 0} \left ({e^x+e^{-x}-2\over x^2} \right )^{1\over x^2}$ Aug29 reviewed Approve suggested edit on Normal Matrix Having all real eigen values is Hermitian Aug29 accepted Normal Matrix Having all real eigen values is Hermitian Aug29 reviewed Approve suggested edit on Eigenvalues for the Sturm-Liouville boundary value problem Aug29 reviewed Approve suggested edit on Normal Matrix Having all real eigen values is Hermitian Aug29 asked Normal Matrix Having all real eigen values is Hermitian Aug22 comment $f:\mathbb{R}^2\to\mathbb{R}^2, f(x,y)=(x+2y+y^2+|xy|,2x+y+x^2+|xy|)$ Okay got it...,.. Aug22 comment $f:\mathbb{R}^2\to\mathbb{R}^2, f(x,y)=(x+2y+y^2+|xy|,2x+y+x^2+|xy|)$ so $3$ and $4$ are true, and $1,2$ are false, but how to show $f$ is differentiable? Aug22 comment $f:\mathbb{R}^2\to\mathbb{R}^2, f(x,y)=(x+2y+y^2+|xy|,2x+y+x^2+|xy|)$ Yes Yes, they wanted which are the correct statements Aug22 asked $f:\mathbb{R}^2\to\mathbb{R}^2, f(x,y)=(x+2y+y^2+|xy|,2x+y+x^2+|xy|)$ Aug21 comment On $f:A\to\mathbb{R}^2, f(x,y)=({x\over 1+x+y},{y\over 1+x+y})$ Oh Yes, I thought they are asking whether determinant of the Jacobian matrix vanishes, anyway the matrix also does not vanish on $A$ Aug21 answered Multivariate limit $\lim_{(x,y) \to (0,0)} \frac{{x{y^2}}}{{{x^2} + {y^4}}} = 0$ Aug21 revised On $f:A\to\mathbb{R}^2, f(x,y)=({x\over 1+x+y},{y\over 1+x+y})$ added 1 character in body Aug21 asked On $f:A\to\mathbb{R}^2, f(x,y)=({x\over 1+x+y},{y\over 1+x+y})$ Aug16 comment Let $f:[-1,1] \to \mathbb{R}$ be differentiable 3 times, prove $\exists M>0 \ , \ s.t \ f(x) \le Mx^2$ Why $f'(0)=0$? Can you explain? Aug13 accepted $x_1,x_2,x_3,x_4$ are in Harmonic Progression $\Rightarrow (x_1-x_3)(x_2-x_4)=4(x_1-x_2)(x_3-x_4)$ Aug13 asked $x_1,x_2,x_3,x_4$ are in Harmonic Progression $\Rightarrow (x_1-x_3)(x_2-x_4)=4(x_1-x_2)(x_3-x_4)$ Aug9 accepted How to find the area of an isosceles triangle without using trigonometry?