Question

Taylor series question: some the coefficients of the powers of x in the Taylor polynomial for the function f(x) = tan(x) are 0. What property of the function tan(x) does this reflect?

Answer 1

first three terms:
\[x^{1} + \frac{1}{3}x^{3} +\frac{2}{15}x^{5}\]

Answer 2

hint:
Foe even functions, f(x) = f(-x)
for odd functions , f(x)= -f(-x)
so what u think? tan is even or odd ?

Answer 3

odd

Answer 4

thats correct if that what u wanted..............................

Answer 5

so it reflects its odd property that all the even powers of x have 0 as a coefficient

Answer 6

yes,i think so , that why even powers are missing