Which of the following is the nth taylor polynomial tn(x) for f(x)=ln(1−x) based at b=0? tn(x) = −x + 1 2 x2 − 1 3 x3−+ 1 n xn tn(x) = −x − x2 − 1 2 x3−− 1 n−1 xn tn(x) = −x − 1 2 x2 − 1 3 x3−− 1 n xn tn(x) = −x − 1 2! x2 − 1 3! x3−− 1 n! xn find the smallest value of n such that taylor's inequality guarantees that |tn(x)−ln(1−x)|< 0.01 for all x in the interval i= − 1 2 , 1 2

The equatorial radius of earth is approximately 6 × 10^3 km, while the equatorial radius of saturn is approximately 6 × 10^4 km. which of the following is true? a. the equatorial radius of saturn is approximately one hundred times that of earth. b. the equatorial radius of saturn is approximately ten times that of earth. c. the equatorial radius of earth is approximately one hundred times that of saturn. d. the equatorial radius of earth is approximately ten times that of saturn.