Recent content by willy0625

This question poped up somewhere in my research. I can use any results in calculus and analysis. Note I have made some correction to the F function.

Yeah showing the uniqueness of that particular point is enough.

Homework Statement How would you go about proving that the functions F(x)=\frac{2}{\pi}\arctan\Big(\frac{x}{a}\Big), x \geq 0 with a > 0 and G(x)=1-\exp(-\lambda x),x\geq0 with \lambda>0meet only at one point for some x > 0 The Attempt at a Solution At x=0, F and G takes the...

Any point in 3-dimensional space Is is possible to write any point {\bf x}\in \mathbb{R}^{3} as a linear combination of vectors {\bf v_{j}} inside the unit ball over \mathbb{R} given that \sum_{j}c_{j}{\bf v_{j}} can be made arbitrarily small? My approach was letting...

I am trying to find the second derivative of the function C:[0,1]^{2} \rightarrow [0,1] ,\quad \mbox{defined by }C=C(u,v) evaluated at u=F(x)=1-\exp(-\lambda_{1} x),\quad \lambda_{1} \geq 0 and v=G(x)=1-\exp(-\lambda_{2} x),\quad \lambda_{2} \geq 0 First I work out the first...