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lim(x→0)tan(x)^2/sin3x求极限,先谢
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lim(x→0)tan(x)^2/sin3x
求极限,先谢
求极限,先谢
▼优质解答
答案和解析
General solution:
lim(x→0) tan²x/sin3x
=lim(x→0) sin²x/cos²x*1/sin3x
=lim(x→0) sin²x/x²*x²/cos²x*3x/sin3x*1/3x
=lim(x→0) (sinx/x)²*(3x/sin3x)*(x/3)
=1²*1*0/3
=0
lim(x→0) tan²x/sin3x
=lim(x→0) sin²x/cos²x*1/sin3x
=lim(x→0) sin²x/x²*x²/cos²x*3x/sin3x*1/3x
=lim(x→0) (sinx/x)²*(3x/sin3x)*(x/3)
=1²*1*0/3
=0
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