Lagrange interpolation from tabulated values

Find a polynomial in $x$, of as low a degree as possible, taking at $x=2, 4, 5, 10$ respectively the values $3, 7, 9, 19$.

Find a polynomial in $x$, of as low a degree as possible, taking at $x=2, 4, 5, 10, 15$ respectively the values $3, 7, 9, 19, 0$.

Find a polynomial in $x$, of as low a degree as possible, taking at $x=1,2,3,4,5$, respectively the values $2, 1, -1, 5, 0$.

Find a polynomial $f(x)$, of as low a degree as possible, taking at $x = -2, -1, 0, 1, 2$ the same values as the function $y = \sin \dfrac {\pi x}{2}$. Determine the value of the difference $f(x) - y$ at the values $x$ equal to $\dfrac {1}{2}, \dfrac {5}{3}, 10$.

Find a polynomial $f(x)$, of as low a degree as possible, taking at $x=-2, -\dfrac {4}{3}, 0, \dfrac {4}{3}, 2$ the same values as the function $y = \cos \dfrac {\pi x}{4}$. Determine the values of the difference $f(x) - y$ at the values $x$ equal to $-1, 3, 10$.