What is the size of the smallest MIS (Maximal Independent Set) of a chain of nine nodes?

$$\mathop {\lim }\limits_{x \to \infty } {{x - \sin x} \over {x + \cos \,x}}\,\,Equals$$

If $$\,\,\,\,f\,\,\,\,\left( x \right)$$ is defined as follows, what is the minimum value of $$f\,\left( x \right)$$ for $$x \in \left( {0,2} \right)$$ ? $$$f\left( x \right) = \left\{ {\matrix{ {{{25} \over {8x}}\,\,when\,\,x \le {3 \over 2}} \cr {x + {1 \over x}other\,wise} \cr } } \right.$$$

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $$3{x^4} - 16{x^3} + 24{x^2} + 37$$ is