高数 求极限 xsin(2/x+1)x->无穷 求 xsin(2/x+1)的极限初学毫无头绪 3Q哈

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高数 求极限 xsin(2/x+1)x->无穷 求 xsin(2/x+1)的极限初学毫无头绪 3Q哈
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高数 求极限 xsin(2/x+1)x->无穷 求 xsin(2/x+1)的极限初学毫无头绪 3Q哈
高数 求极限 xsin(2/x+1)
x->无穷 求 xsin(2/x+1)的极限
初学毫无头绪 3Q哈

高数 求极限 xsin(2/x+1)x->无穷 求 xsin(2/x+1)的极限初学毫无头绪 3Q哈

答:
lim(x→∞) xsin[2/(x+1)]
=lim(x→∞) sin[2/(x+1)] / [1/(x+1)]
=lim(x→∞) 2 sin[2/(x+1)] /[2/(x+1)] 令t=2/(x+1)→0
=lim(t→0) 2sin t /t
=2

x->无穷 求 xsin(2/x+1)
原式=lim(x->∞)sin(2/x+1)/(1/x)
=lim(x->∞)sin(2/x+1)/(2/x+1)*
=lim(x->∞)2x/x+1
=2

(x+1)sin2/x+1 -sin/x+1=(x+1)2/x+1-0=2