已知函数f(x)=14x4-23x2+6,则limn→∞f(x+1)-f(x)2x3=______.-数学

题目简介

已知函数f(x)=14x4-23x2+6,则limn→∞f(x+1)-f(x)2x3=______.-数学

题目详情

已知函数f(x)=
1
4
x4-
2
3
x2+6,则
lim
n→∞
f(x+1)-f(x)
2x3
=______.
题型:填空题难度:偏易来源:不详

答案

f(x)=class="stub"1
4
x4-class="stub"2
3
x2+6
f(x+1)-f(x)
2x3
=
class="stub"1
4
(x+1)4-class="stub"2
3
(x+1)2+6-class="stub"1
4
x4+class="stub"2
3
x2-6 
2x3
=
x3+ class="stub"3
2
x2-class="stub"1
3
x-class="stub"5
12
  
2x3
=
1+class="stub"3
2x
-class="stub"1
3x2
-class="stub"5
12x3
2

lim
n→∞
f(x+1)-f(x)
2x3
=
lim
n→∞
1+class="stub"3
2x
-class="stub"1
3x2
-class="stub"5
12x3
2
=class="stub"1
2

所以
lim
n→∞
f(x+1)-f(x)
2x3
=class="stub"1
2

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