求下列极限:(1)limn→∞2n2+n+75n2+7;(2)limn→∞(n2+n-n);(3)limn→∞(2n2+4n2+…+2nn2).-数学

题目简介

求下列极限:(1)limn→∞2n2+n+75n2+7;(2)limn→∞(n2+n-n);(3)limn→∞(2n2+4n2+…+2nn2).-数学

题目详情

求下列极限:
(1)
lim
n→∞
2
n
+n+7
5n2+7

(2)
lim
n→∞
n2+n
-n);
(3)
lim
n→∞
2
n2
+
4
n
+…+
2n
n2
).
题型:解答题难度:中档来源:不详

答案

(1)
lim
n→∞
2n2+n+7
5n2+7
=
lim
n→∞
2+class="stub"1
n
+class="stub"7
n2
5+class="stub"7
n
=class="stub"2
5

(2)
lim
n→∞
n2+n
-n)=
lim
n→∞
class="stub"n
n2+n
+n
=
lim
n→∞
class="stub"1
1+class="stub"1
n
+1
=class="stub"1
2

(3)原式=
lim
n→∞
class="stub"2+4+6++2n
n2
=
lim
n→∞
n(n+1)
n2
=
lim
n→∞
(1+class="stub"1
n
)=1.

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