Question

求解极限！！

Answer 1

(1)
lim<n→∞>(n/2)R²sin(2π/n)极限不存在

(3)
lim<x→0>arctan3x/sin2x
=lim<x→0>(arctan3x)'/(sin2x)'
=lim<x→0>[3/(1+9x²)]/(2cos2x)
=[3/(1+0)]/(2×1)
=3/2

(5)
lim<x→0>(1-cos4x)/(xsinx)
=lim<x→0>[1-(1-2sin²2x)]/(xsinx)
=lim<x→0>2sin²2x/(xsinx)
=lim<x→0>2(2sinxcosx)²/(xsinx)
=lim<x→0>8sin²xcos²x/(xsinx)
=lim<x→0>8sinx/x
=8

(1)
lim<x→∞>[x/(1+x)]^(x-3)
=lim<x→∞>[1-(1/1+x)]^(x-3)
=lim<x→∞>{[1+(-1/1+x)]^-(1+x)}^[(x-3)/-(1+x)]
=e^lim<x→∞>[(-x+3)/(x+1)]
=e^(-1)
=1/e

(2)
lim<x→∞>[(2x+1)/(2x-1)]^x
=lim<x→∞>[(2x-1+2)/(2x-1)]^x
=lim<x→∞>[1+2/(2x-1)]^x
=lim<x→∞>{[1+2/(2x-1)]^(2x-1/2)}^[2x/(2x-1)]
=e^lim<x→∞>[2x/(2x-1)]
=e

(3)
lim<x→0>(1+2tanx)^cotx

=lim<x→0>[(1+2tanx)^(1/2tanx)]^(2tanx*cotx)
=e²

追问

你好样儿的

第一题第一问错了

Answer 2

太多了，用等价无穷小或两个重要极限

追问

那你帮我做下第二题的1.3吧

追答