What is $\lim\limits_{x \to 1}\frac{x^3 - 1}{\sqrt x - 1}$ equal to?

In which one of the following intervals is the function $f(x) = \frac{x^3}{3}-\frac{7x^2}{2} + 6x + 5$ decreasing?

If the derivative of the function$f(x) =\frac{m}{x} +2nx + 1$ vanishes at x = 2, then what is the value of m + 8n ?

What is the area included in the first quadrant between the curves y = x and y = x³ ?