Mathematical functions

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

1. \(f(x) = \frac{5}{2}x^4 + \frac{x^2}{6} + 7\).

   See the following examples:

   >>> a = f(0.0)
   >>> print(round(a, 4))
   7.0
   >>> print(round(f(10.1), 4))
   26039.1019
   >>> print(round(f(-1.4), 4))
   16.9307
   >>> print(round(f(6.0), 4))
   3253.0
   >>> print(round(f(-0.12345), 4))
   7.0031
   

   Note

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

2. \(g(x)= \frac{(3x-2)}{2} + \frac{(x-7)^3}{7} + 2\)

   See the following examples:

   >>> print(round(g(0.0), 4))
   -48.0
   >>> print(round(g(7.0), 4))
   11.5
   >>> print(round(g(1.2345), 4))
   -24.527
   >>> print(round(g(-123.45), 4))
   -317311.8987
   >>> print(round(g(2.222), 4))
   -11.2496
   

   Note

   More tests are providedin the test-funcmat2.txt file.

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

   See the following examples:

   >>> print(round(h(0.0, 0.0), 4))
   -0.0
   >>> print(round(h(45.0, 1.99), 4))
   -35.2667
   >>> print(round(h(90.0, 0.0), 4))
   -0.0
   >>> print(round(h(-90.0, 2.4), 4))
   -1.3636
   >>> print(round(h(360.0, 0.0), 4))
   0.0
   

   Note

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

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

4. \(k(x)= \sqrt{f(x)}-g(x^2)\). This function must call the previous ones

   See the following examples:

   >>> print(round(k(0.0), 4))
   50.6458
   >>> print(round(k(2.0), 4))
   3.7612
   >>> print(round(k(-20.0), 4))
   -8671176.6291
   >>> print(round(k(9.876), 4))
   -106005.465
   >>> print(round(k(0.00836345), 4))
   50.6442
   >>> print(round(k(-1.01111), 4))
   31.108
   

   Note

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

Solutions

A solution of these functions is provided in the funcmat.py file.