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1. Without using L'Hopital's rule, evaluate the following limits of sequences. Fur- thermore, if the limit does not exist but diverges to , please indicate

1. Without using L'Hopital's rule, evaluate the following limits of sequences. Fur- thermore, if the limit does not exist but diverges to , please indicate so and determine the correct sign. (a) lim(sqrt (n^2 +n) - sqrt (n^2 1)) n (b) lim (sin(n) + cos(n^2))/(n-100)) n

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