# How to solve the following special inequality?

Find $k$, as a function of $d_2$ and $d_3$, such that:

$$\left \vert { d_2 \left [ \sin(e^{d_3\,y}) - \sin(e^{d_3\,x})\right] + (x-y) d_2 d_3 e^{d_3\,z} \cos(e^{d_3\,z})} \right \vert \le k (\vert{x-z}\vert + \vert{y-z}\vert) \,\vert{x-y}\vert$$

-
hell of the inequality :D –  Neo Nov 23 '12 at 20:03
hell of what? i voted it as an useful comment because this comment makes me laugh. i do not know why –  Mia Nov 23 '12 at 20:09
I see that k appears only on RHS. Why don't you divide the inequality by the number multiplied by k –  Amr Nov 23 '12 at 20:22

Without further restrictions, there can be no such $k$. As $z\to\infty$ (if $d_3>0$) or $z\to-\infty$ (if $d_3<0$) the $\limsup$ the left side is $\Theta(e^{d_3z})$, whereas the right side is $\Theta(|z|)$.