John Wayland Bales

 34 proof of $\log(xy) =\log (x) + \log (y)$ 16 Why does $3^{16} \times 7^{-6}$ become $\frac{3^{16}} {7^{6}}$? 15 How to integrate $|x| \cdot x$ 12 How many whole pieces can be taken out in this way? (Infinite chocolate bar problem) 12 How can points that have length zero result in a line segment with finite length?

### Reputation (17,532)

 +10 simplification of quadratic standard form equation +20 Convergence of $\int_{x=0}^\infty x^8 e^{-\sqrt x} dx$ +10 The Meaning of the partial derivative given the graph +10 $dy/dx$ problems, please help

### Questions (11)

 8 Simple proof of area of “rectangled” circle 5 Solutions to $(x+y)f(x+y)=xf(x)+yf(y)$ 4 “Proving” the definition of the Laplace Transform from two properties 4 Given $f(z)=\dfrac{U(z)}{V(z)}=\dfrac{2z^3-3z^2+7z-8}{z^4-5z^3+4z^2-6z+1}$ find $f(1-\sqrt{2}i)$ without lots of complex arithmetic. 3 Solution of $ty'' +(2t+3)y' +(t+3)y = 3e^{-t}$ via Laplace transform

### Tags (253)

 255 calculus × 195 98 trigonometry × 74 199 algebra-precalculus × 109 84 ordinary-differential-equations × 62 137 integration × 76 75 functions × 53 104 real-analysis × 61 63 logarithms × 12 100 geometry × 57 54 multivariable-calculus × 39

### Bookmarks (13)

 10 If $f(x)^2=x+(x+1)f(x+2)$, what is $f(1)$? 8 Proof that $x^y + y^x > 1 \ \forall x,y > 0$ [duplicate] 5 Proving by induction of $n$ that $\sum_{k=1}^n \frac {k+2}{k(k+1)2^{k+1}} = \frac{1}{2} \ - \frac1{(n+1)2^{n+1}}$ 3 proving $\cos (A+B)>0$, if given angles $A$ and $B$ 3 For $P$ an arbitrary point in $\triangle ABC$, show that $\sum_{cyc}c(\sin \angle CAP+\sin\angle CBP)\leq a+b+c$