even and odd cubic polynomials
By Sarah Richards
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Book says approximating even function $P_3$ must be of form $ax^2+b\ $so they neglected $x,x^3\ $. This function approximate even function $|x|^3$very nicely in the book after some tweaking.
I am thinking if I was to approximate an odd fuction with polynomial of degree 3 should I ditch term $x^2\ $ and have it as $ax^3 + bx + c\ $When I draw this function it make sense.
Here is the graph of modified polynomial and 2 odd functions $x^3\ $ and $sin x$.
