Page 31 - e-book Calculcs I

14. จงหาลิมิต lim →0 (1 + ) 1 ⁄

ให้ = (1 + ) 1 ⁄

1
ln = ln(1 + ) = ln(1+ )

lim →0 ln = lim →0 ln(1+ )

= lim →0 1/(1+ )
1
= 1

1
∴ lim →0 (1 + ) 1 ⁄ = = 1

15. จงหาลิมิต lim →+∞ (√ + − )
2
2
2
2
lim →+∞ (√ + − ) = lim →+∞ (√ + − ) ( √ + + )
2
√ + +
2
= lim →+∞ + − 2
2
√ + +
1
= lim →+∞ 2 +1 +1
2
2√ +
พิจารณา lim →+∞ 2 +1
2
2√ + 1
lim →+∞ 2 +1 = lim →+∞ 2+ ⁄
2
1
2√ + 2√1+ ⁄
2+0
=
2√1+0
= 1
1
2
∴ lim →+∞ (√ + − ) =
2

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