The function f(x) = 10x ln(1 + x) is represented СО f(x) = Σ ca". n=0 Find the specified coefficients in the power series. C2 = C3= C4= C5 C6 Find the radius of convergence R of the series. R=

Find the interval of convergence of the power series E-12 en(x - 2)".

Find the Maclaurin series forf(x) = 1/(6-x-x2)and determine its radius of convergence. You must find an explicit expression for the coefficients in the power series.

f(x) = 5xsin(x') Find the first three nonzero terms of the Maclaurin series for by using an appropriate substitution in a known Maclaurin series and performing any algebraic operations that are required. State the radius of convergence of the series.

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)* +...