The Fibonacci series is defined by the equations:

Fk+1=Fk +Fk−1, for k=2,3,4,…,n

 

where F2=F1=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, Fk for k = 1,2,…,10. Use the MATLAB function fimplicit to provide a plot of the two-dimensional implicit function:

Cos (x2 +y)+ 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 (x2 + y2 +z2) − x2 y2 z2 = 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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