use the epsilon N defintion of limit to show lim of 2n/(sqrt(4n^2 + n + 1) = 1

Question

David · Accepted Answer

For given � > 0 suppose
| 2n√
4n2 + n+ 1
− 1|  0
Let us factor 4n2(�1 − 1) + �1n+ �1 = 0 we have
n =
−�1 ±
√
�21 − 16�21 + 16
8(�1 − 1)
That is we must have
(n− (−�1 +
√
�21 − 16�21 + 16
8(�1 − 1)
))(n− (−�1 −
√
�21 − 16�21 + 16
8(�1 − 1)
)) > 0
That is
n >
−�1 +
√
�21 − 16�21 + 16
8(�1 − 1)
= N
1

use the epsilon N defintion of limit to show lim of 2n/(sqrt(4n^2 + n + 1) = 1

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment