10 (1 - 6x)² convergence R Represent the function Co= C1 = C2 = C3 C4 = Find the radius of || as a power series f(x) = Σ n=0 = спосп

x-5 4) Let f(x) = х2-1 Find a Power Series for_f(x) centered at c= 0 and its interval for convergence Hint: Partial Fractions

Find the range of values of the variable x for which the following geometric power series converges: (interval of convergence) a) G(x)=1+3x+9x² + 27x³ +81x* +... b) G(x)=1-*=1, (x-1)' _ (x-1)³ , (x-1)* 4 х-1, (х-1)* b) G(x) =1-: 2 +... 8 16 c) G(x)=1+0.4(x+3)+0.16(x+ 3)² +0.064(x+3)³ +0.0256(x+3)* +...

The function f is defined by the power series (-1)" x²n f(x) = Σ n=0 (2n+1)! for all real numbers x. Use the first and second derivative test by finding f'(x) and f"(x). Determine whether f has a local maximum, a local minimum, or neither at x=0. x4 1+1-1 5! = 1 −²+ 3! 7! +. + (-1)"x²n (2n+1)!