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Calculate if the limit exists and explain why it does not do so for the rest, for the following cases: c < −1 ; c = −1 ; −1 < c < 0 ; c = 0 ; 0 < c < 1 ; c = 1 ; c > 1
For c<−1 The expression does not have a limit.
Altough the absolute value diverges to , the terms cn alternate in sign.For c=−1 The expression does not have a limit.
Altough the absolute value remains constant (=1), the terms cn alternate in sign.For −1<c<0 =0 .
For c=0 =0 .
For 0<c<1 =0 .
For c=1 =1 .
For c>1 = .
Part 1 is divided in two : answer and explaination. Each one is worth 1 point.
Part 2 is divided in two : answer and explaination. Each one is worth 1 point. Part 3 is not divided, but is more difficult. It is worth 2 points. Parts 4, 5, 6, 7 are each worth 1 point.