calculus week5

Congratulations! You passed! Grade received 100% Latest Submission Grade 100% To pass 60% or higher Go to next item 1. Question 1 Use the geometric series to compute the Taylor series for ( )=12− � � � f ( x )=2− x 1 . Where does this series converge? Hint: 12− =1211− 2 � � 2− x 1=211− 2 x 1 1 / 1 point Correct 2. Question 2 Compute and simplify the full Taylor series about =0 � x =0 of the function ( )=12− +12−3 � � � � f ( x )=2− x 1+2−3 x 1 . Where does this series converge? 1 / 1 point Correct 3. Question 3 Which of the following is the Taylor series of ln11− � ln1− x 1 about =0 � x =0 up to and including the terms of order three? 1 / 1 point Correct 4. Question 4 Use the binomial series to find the Taylor series about =0 � x =0 of the function ( )=(9− 2)−1/2 � � � f ( x )= ( 9− x 2 ) −1/2 . Indicate for which values of � x the series converges to the function. 1 / 1 point Correct 5. Question 5 Use the fact that arcsin =∫ 1− 2 � �� � arcsin x = ∫ 1− x 2 dx and the binomial series to find the Taylor series about =0 � x =0 of arcsin � arcsin x up to terms of order five. 1 / 1 point Correct 6. Question 6 Compute the Taylor series about =0 � x =0 of the function arctan( −1) �� arctan( e x −1) up to terms of degree three. 1 / 1 point Correct 7. Question 7