Differentiate the given series expansion of f term-by-term to obtain the corresponding series expansion for the derivative of f . 1 If f(x) = = 1+8x ∞ (-1)"8"x" -(-1 = n=0 ∞ f'(x) = Σ n=1

Find the power series for the function f(x)=(12x)/(x+1) using the power series for 1/(x+1).

Q5: a\. Let f(x) = x³ - 3x² - 1,x2 2. State and prove the theorem of derivative of inverse functions and use them to find the value of df-1/dx at the point x = -1 = f(3). b\ Write the Pascal's triangle for values of n = 6, then use it to determine the binomial series expansion of (3 - 2x)6, and simplify the result.

Q1/ Find the Fourier series for the Function f(x) = 4 - X2 ,When   - 2 <X< 2

Let f(x) be the function which is represented by the power series : f(x)= En=1 (-1)"(x-2)" Find the 5th derivative of f(x) at x = 1