(1) The iterative scheme #x_{n+1}=\frac{1}{2}\left(x_{n}+\frac{a}{x_{n}}\right)# converges to #\sqrt{a}#. The convergence is

linear
quadratic
cubic
bi-quadratic

(2) The fourth order divided difference of the polynomial #3x^{3}+11x^{2}-5x+11# over the points #x=0, 1, 4, 6\textrm{ and }7# is

#18#
#11#
#3#
#0#

(3) What is the degree of polynomial of least degree which takes the following data? #\\\hspace{20pt}\begin{array}{|c|c|c|c|c|c|c|}\hline x & 0 & 1 & 2 & 3 & 4 & 5\\\hline f(x) & 0 & 3 & 8 & 15 & 24 & 35\\\hline \end{array}#

#4#
#2#
#3#
#5#

(4) The trapezoidal rule applied to #\int\limits_{1}^{3}f(x)dx# gives the value #8# and Simpson's rule gives the value #4#. What is #f(2)#?

#2#
#0#
#1#
#3#

(5) A polynomial #p(x)# satisfies the following: #p(1)=p(3)=p(5)=1, p(2)=p(4)=-1#. Then the minimum degree of such a polynomial is

#1#
#2#
#3#
#4#