高数求极限 帮下忙1.Lim X趋向0,SIN5X^2/(TAN2x)^22.Lim X趋向PAi SINX/X-PAI
来源:学生作业帮 编辑:拍题作业网作业帮 分类:数学作业 时间:2024/04/29 21:09:06
高数求极限 帮下忙
1.Lim X趋向0,SIN5X^2/(TAN2x)^2
2.Lim X趋向PAi SINX/X-PAI
3 Lim X趋向正无穷,2^x*SIN 1/2^X
大家不要嘲笑我-,
1.Lim X趋向0,SIN5X^2/(TAN2x)^2
2.Lim X趋向PAi SINX/X-PAI
3 Lim X趋向正无穷,2^x*SIN 1/2^X
大家不要嘲笑我-,
lim(x->0) sin5x^2/(tan2x)^2 【等价无穷小替换:sint~t,tant~t】
①=lim(x->0) 5x^2/(2x)^2
=5/4
②=lim(x->0) sin5x^2/[sin2x/cos2x]^2
=lim(x->0) [sin5x^2/5x^2]* 5/4*[[2x/sin2x]^2]*[cos2x]^2
=5/4
①lim(x->π) sinx/(x-π) 【0/0 ,罗必塔法则】
=lim(x->π) cosx/1
=-1
②lim(x->π) sinx/(x-π) 【令:π-x = t】
=lim(t->0) sin(π-t)/(-t)
=-lim(t->0) sint/t
=-1
①lim(x->+∞) 2^x*sin(1/2^x) 【等价无穷小替换:x->+∞,1/2^x ->0,sin(1/2^x)~1/2^x】
=lim(x->+∞) 2^x*(1/2^x)
=1
②lim(x->+∞) 2^x*sin(1/2^x)
=lim(x->+∞) sin(1/2^x) /[1/2^x] 【令:1/2^x=t】
=lim(t->0) sint/t
=1
①=lim(x->0) 5x^2/(2x)^2
=5/4
②=lim(x->0) sin5x^2/[sin2x/cos2x]^2
=lim(x->0) [sin5x^2/5x^2]* 5/4*[[2x/sin2x]^2]*[cos2x]^2
=5/4
①lim(x->π) sinx/(x-π) 【0/0 ,罗必塔法则】
=lim(x->π) cosx/1
=-1
②lim(x->π) sinx/(x-π) 【令:π-x = t】
=lim(t->0) sin(π-t)/(-t)
=-lim(t->0) sint/t
=-1
①lim(x->+∞) 2^x*sin(1/2^x) 【等价无穷小替换:x->+∞,1/2^x ->0,sin(1/2^x)~1/2^x】
=lim(x->+∞) 2^x*(1/2^x)
=1
②lim(x->+∞) 2^x*sin(1/2^x)
=lim(x->+∞) sin(1/2^x) /[1/2^x] 【令:1/2^x=t】
=lim(t->0) sint/t
=1
高数求极限 帮下忙1.Lim X趋向0,SIN5X^2/(TAN2x)^22.Lim X趋向PAi SINX/X-PAI
求极限,lim x趋向于pai/2-0 cosx的pai/2 -x次方
lim(sinx)^tanx (x趋向于pai/2)
帮我求下列极限:lim(x趋向于0)tan2x/sin5x;得有过程
x趋向0 lim cos(1/x),x趋向pai/2 tanx
求极限lim[sinx/(x-pai)] x趋于pai
求极限:lim(sinx)^tanx (x趋近于pai/2)
lim ln(sinx/x)的极限.x趋向于0
求极限,lim(x趋向于0+)(根号(1+tan2x)-根号(1-tan2x))/sin3x
lim x趋向0 x^2-sinx/x+sinx
1.x趋向0 lim (cosx-1)/x 2.x趋向0 lim sinx/x
求极限当x趋向π,lim(x^2-π^2)/sin5x