求x→∝ sin^2 ax/x^2的极限

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/18 02:28:31
求x→∝sin^2ax/x^2的极限求x→∝sin^2ax/x^2的极限求x→∝sin^2ax/x^2的极限x趋于无穷则sin²(ax)在[0,1]震荡即有界,而分母趋于无穷所以极限=0应该

求x→∝ sin^2 ax/x^2的极限
求x→∝ sin^2 ax/x^2的极限

求x→∝ sin^2 ax/x^2的极限
x趋于无穷则sin²(ax)在[0,1]震荡
即有界,而分母趋于无穷
所以极限=0

应该是0,因为x趋近无穷大
sin²永远在[0,1]
而x²会无穷增大
要是趋近于0就不一样了,得到a²

lim(x→∝ )-1/x^2 <=lim(x→∝ )(sinx)^2/x^2 <=lim(x→∝ )1/x^2
0<=lim(x→∝ )sinx^2/x^2<=0
lim(x→∝ )(sinx)^2/x^2=0