Question: I have to find the volume of the solid $\Omega$ which is bounded by the paraboloids
$$z=x^{2}+y^{2},\quad z=4x^{2}+4y^{2}$$
by the planes
$$y=\sqrt{3}x,\quad y=\frac{\sqrt{3}}{3}x$$
and by the cylinders
$$x^{2}+y^{2}=1,\quad x^{2}+y^{2}=4$$
I draw it here: [Omega](https://ggbm.at/s53t4u5q) and I really have no idea how to find the limits of integration for $x,y$ and $z$. Actually, I can't even see what region is $\Omega$.

Answer: 
using the fact that $\lim \_{ x\rightarrow 0 }{ \frac { \sin { x } }{ x } } =1\\ $ we get 
$$\lim \_{ x\rightarrow 1 }{ \frac { \sin { \left( 3{ x }^{ 2 }-5x+2 \right) } }{ { x }^{ 2 }+x-2 } } =\lim \_{ x\rightarrow 1 }{ \frac { \sin { \left( 3{ x }^{ 2 }-5x+2 \right) } }{ 3{ x }^{ 2 }-5x+2 } \frac { 3{ x }^{ 2 }-5x+2 }{ { x }^{ 2 }+x-2 } } =\\ =\lim \_{ x\rightarrow 1 }{ \frac { \left( x-1 \right) \left( 3x-2 \right) }{ \left( x+2 \right) \left( x-1 \right) } } =\frac { 1 }{ 3 } $$
Hint:
$$
\frac{\sin(3x^2 - 5x + 2)}{x^2+x-2} = \frac{\sin(3x^2 - 5x + 2)}{3x^2 - 5x + 2}\cdot \frac{3x^2 - 5x + 2}{x^2+x-2}.
$$