The Fibonacci series is deﬁned by the equations:

F_{k+1}=F_{k} +F_{k−1}, for k=2,3,4,…,n

where F_{2}=F_{1}=1.

Write a MATLAB recursive function to evaluate the elements of this series to any number of steps n. Use this function to produce a table of the values of the Fibonacci series, F_{k} for k = 1,2,…,10. Use the MATLAB function fimplicit to provide a plot of the two-dimensional implicit function:

Cos (x^{2} +y^{2 })+ xy = 0

for values of x and y in the range x=−4 to 4;y=−4 to 4.For the three-dimensional implicit function

sin (x^{2} + y^{2} +z^{2}) − x^{2} y^{2} z^{2} = 0

use the MATLAB function fimplicit 3 to plot this function for x and y in the range x=−4to4; y=−4 to 4.

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