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-PAI3 Lim X趋向正无穷,2^x*SIN 1/2^X大家不要嘲笑我-,
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![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-PAI3 Lim X趋向正无穷,2^x*SIN 1/2^X大家不要嘲笑我-,](/uploads/image/z/9299142-54-2.jpg?t=%E9%AB%98%E6%95%B0%E6%B1%82%E6%9E%81%E9%99%90+%E5%B8%AE%E4%B8%8B%E5%BF%991.Lim+X%E8%B6%8B%E5%90%910%2CSIN5X%5E2%2F%28TAN2x%29%5E22.Lim+X%E8%B6%8B%E5%90%91PAi+SINX%2FX-PAI3+Lim+X%E8%B6%8B%E5%90%91%E6%AD%A3%E6%97%A0%E7%A9%B7%2C2%5Ex%2ASIN+1%2F2%5EX%E5%A4%A7%E5%AE%B6%E4%B8%8D%E8%A6%81%E5%98%B2%E7%AC%91%E6%88%91-%2C)
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-PAI3 Lim X趋向正无穷,2^x*SIN 1/2^X大家不要嘲笑我-,
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-,
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-PAI3 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