Question 1:

Let cota(@ - a) + co(@ - a)'+ + en(@ - a)" be the Taylor series of the function f(@) = asin(@). For a = 0 determine the value of C3. C3For the following function, find the Taylor series centered at : = and then give the first 5 nonzero terms of the Taylor series and the open interval of convergence. f(x) = sin(x) + + + ... The open interval of convergence is: (Give your answer in interval notation.)The function f(@) = sin(8x) has a Maclaurin series. Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with 4 nonzero terms.Use the following binomial series formula (1 + x)" =1+mat m(m - 1) 2 + ...+ m(m - 1) . . . (m - k +1) k + . . 2! k! to obtain the MacLaurin series for (a) (1+z)* (b) VI+ = O + . ... Enter first 4 terms only.dy Solve = (y - 1)(y + 1) if the solution passes through the point (@, y) = (1, 0). Graph the solution. y(@) = help (formulas)