求极限,麻烦各位写清楚拍过来,

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求极限,麻烦各位写清楚拍过来,
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求极限,麻烦各位写清楚拍过来,
求极限,麻烦各位写清楚拍过来,
 

求极限,麻烦各位写清楚拍过来,
lim xsin(1/x)
=lim sin(1/x)/(1/x)        设 t = 1/x.当 x→∞时,t → 0
=lim sint/t
=1
lim√(1-cosx)/|x|
=lim|√2*sin(x/2)|/|x|        注:1-cosx = 2[sin(x/2)]^2
=2√2*lim|sin(x/2)/(x/2)|
=2√2*| lim sin(x/2)/(x/2) |
=2√2 * 1
=2√2