(a) Use differentiation to find a power series representation for fx) = (3 + x)2" Σ 00 n = 0 What is the radius of convergence, R? R%3D (b) Use part (a) to find a power series for 1 f(x) = (3 + x)3 F(x) = n = 0 What is the radius of convergence, R? (c) Use part (b) to find a power series for x2 f(x) = (3 + x)3 %3D 00 Σ( f(x) = n = 2 What is the radius of convergence, R? R = Need Help? Read it Watch i

Using 1/(1-x), find a power series for f(x)= 3/(2x+5) and its interval of convergence. Write step by step.

To create a power series for the 1 function f(x): = series for f(x)= (5-x)4 1 (5-x)³' O Differentiate the series for 1 f(x) = (5-x)³ result by -1. O Differentiate the series for 1 f(x) = (5-x)³ result by 3. Differentiate the series for 1 f(x) = (5-x)³ result by 3. O Differentiate the series for 1 f(x) = (5-x)³ result by -3. O Differentiate the series for 1 f(x) = (5-x)³ result by -3. None of these. = from the we could then multiply the then multiply the then divide the then multiply the then divide the 2

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)* +...