let f(x) be the power series for sins, centered at x=0. Decide whether f(x^2), f(square root of x), or f(e^x) are power series. Explain your answer.
Power of series of f(g(x)) can be obtained by substituting x with g(x) in the Power series of f(x)
BUT, Power series contains polynomial terms, you cannot have a term which is not polynomial.
Note that f(x^2) is a power series , while f(sqrt(x)) and f(e^x) are not power series for this reason.
Although we should be able to write power series by other methods for these functions too