Find the exact value of 

i) \(\dfrac{1}{3}x^3-5=7\)
ii) \(\dfrac{x^3}{2}+8=19\)

Solve the following

i) \((x+1)^3=8\)
ii) \(2(x-1)^3=-250\)

Sketch the graph of \(y=x^3+1\) in the domain \(-2 \le x \le 2\)

Sketch the graph of \(y=(x-2)^3\) in the domain \(0 \le x \le 4\)

The line \(x=-2\) and \(y=-x^3+6\) intersect at \(P\). Find the coordinates of \(P\)

The line \(y=3\) and \(y=2x^3+1\) intersect at \(P\). Find the coordinates of \(P\)

The graph represents a cubic curve in the form \(y=ax^3+c\). 

The points \((0,1)\) and \((-1,5)\) lie on the curve. 

Find the equation of the curve. 

The graph represents a cubic in the form \(y=ax^3+c\). 

The points \((2,0)\) and \((-1,-9)\) lie on the curve. 

Find the equation of the cubic curve. 

The graph represents a cubic in the form \(y=ax^3+c\). 

The points \((-1,6)\) and \((2,-12)\) lie on the curve. 

Find the equation of the cubic curve.