We have the function : $f(x)=\cos(x) + \sin(x)$ and $x_0=0, x_1=0.25 , x_2=0.5, x_3=1$
a)Find Lagrange polynomial for this function.
c)Find the real approximation error.
d)Find the limit of the maximum error in $[x_0, x_3]$
Dont ask me why there isnt b).Theres no b) in my book. I have solved a and d .Please check them out.Thing is I dont know how to solve c) Here are my solutions.
EDIT : THeres a problem in my lagrange polynom but I dont know what...because my solution is different to this http://www.wolframalpha.com/input/?i=interpolating+polynomial+%7B0%2C1%7D%2C%7B0.25%2C+1.2163%7D%2C%7B0.5%2C+1.357%7D%2C%7B1%2C+1.3817%7D