Mathematical functions
======================

Write and save the Python functions, corresponding to the
following mathematical functions into the same file named
:file:`funcmat.py`. Use the same name of the mathematical functions as the
name of the Python function.

#. :math:`f(x) = \frac{5}{2}x^4 + \frac{x^2}{6} + 7`.
   
   See the following examples:

   .. literalinclude:: test-funcmat1.txt
      :language: python3
      :lines: 3-

   .. note::

      More tests are provided in the :download:`test-funcmat1.txt` file.


#. :math:`g(x)= \frac{(3x-2)}{2} + \frac{(x-7)^3}{7} + 2`
   
   See the following examples:

   .. literalinclude:: test-funcmat2.txt
      :language: python3
      :lines: 3-

   .. note::

      More tests are providedin the :download:`test-funcmat2.txt` file.

#. :math:`h(x,y) = \frac{y \sin x}{y^2-4}`. Supose that `x` is in degrees.

      See the following examples:

   .. literalinclude:: test-funcmat3.txt
      :language: python3
      :lines: 3-

   .. note::

      Moer tests are provided in the :download:`test-funcmat3.txt` file.

   Analyze what will happen if we test this function with point (1,2).

#. :math:`k(x)= \sqrt{f(x)}-g(x^2)`. This function **must call the
   previous ones**

   See the following examples:

   .. literalinclude:: test-funcmat4.txt
      :language: python3
      :lines: 3-

   .. note::

      More tests are provided in the :download:`test-funcmat4.txt` file.


.. rubric:: Solutions

A solution of these functions is provided in the
:download:`funcmat.py<solutions/funcmat.py>` file.