Write a python program to calculate the value of sin(?) using
its Taylor series expansion: sin(?) = ? − ? 3 3! + ? 5 5! − ? 7 7!
+ ? 9 9! … The program should consist of the following
functions:
a) Develop and test a calcSin() function that receives as an
argument, of type float, the value of the variable and returns the
result as a float also. Include 20 terms maximum from the series,
or until...
Find the first four terms in the Taylor series expansion of the
solution to
a. y′(x)=y(x)−x,y(0)=2.
b. y′(x)=2xy(x)−x3,y(0)=1.
c. (1+x)y′(x)=py(x),y(0)=1.
d. y′(x) = ?x2 + y2(x), y(0) = 1.
e. y′′(x)−2xy′(x)+2y(x)=0,y(0)=1,y′(0)=0.
Use the definition of Taylor series to find the first three
nonzero terms of the Taylor series (centered at c) for the
function f.
f(x) = 7 tan x, c = 9π