3) Let $$ F(x)=int _{0}^{x} frac{ln (1+t)}{t} d t $$ (a) Find the Maclaurin series for...

 

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3) Let $$ F(x)=\int _{0}^{x} \frac{\ln (1+t)}{t} d t $$ (a) Find the Maclaurin series for F: (b) Use the series in part (a) to evaluate $F(-1)$ exactly and use the result to state its interval of convergence. (c) Approximate $F\left(\frac{1}{2} ight)$ to three decimals. (Hint: Look for an alternating series. ) CS.VS. 1374 3) Let $$ F(x)=\int _{0}^{x} \frac{\ln (1+t)}{t} d t $$ (a) Find the Maclaurin series for F: (b) Use the series in part (a) to evaluate $F(-1)$ exactly and use the result to state its interval of convergence. (c) Approximate $F\left(\frac{1}{2} ight)$ to three decimals. (Hint: Look for an alternating series. ) CS.VS. 1374