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lim(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) ...

`lim_(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) ` is equal to

(a)0

(b) 2

(c) 4

(d) `oo`

A

1

B

0

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(ntooo)lim(n(2n+1)^(2))/((n+2)(n^(2)+3n-1))=underset(ntooo)lim((2+(1)/(n))^(2))/((1+(2)/(n))(1+(3)/(n)-(1)/(n^(2))))`
`=((2+0)^(2))/((1+0)(1+0+0))=4`
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