Limit of a sequence

1003047301

Level: 
A
Which of the following expressions describes the correct calculation of the limit? L=limn→∞n3+2n−32n3+5
L=limn→∞1+2n2−3n32+5n3=12
L=∞3+2⋅∞−32⋅∞3+5=∞
L=∞3+2⋅∞−32⋅∞3+5=0
L=limn→∞n(n2+2)−32n3+5=−35
L=limn→∞(n2+3)(n−1)2(n3+52)=0

1003047302

Level: 
A
Choose the best first step to take in order to evaluate the limit of the following sequence. (4n5+n4−n3+27n4−2n2+7n)n=1∞
We factor out n4 in the numerator and in the denominator separately.
We factor out n5 in the numerator and in the denominator separately.
We factorize a polynomial in the denominator.
We divide the denominator by n4.
We divide the numerator by n5.