lim(x→0)(sin5x)/x=?

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lim(x→0)(sin5x)/x=?
lim(x→0)(sin5x)/x=?

lim(x→0)(sin5x)/x=?
lim(x→0)(sin5x)/x
=lim(x-->0)5(sin5x/(5x)
=5lim(x-->0)(sin5x)/(5x)
=5*1
=5

lim(x→0)(sin5x)/x
= lim(x→0) (sin5x) / (5x/5)
= 5 lim(x→0)(sin5x) /(5x)
= 5

无穷小代换
lim(x→0)(sinx)/x=1
那么同理
lim(x→0)(sin5x)/x
=lim(x-->0)5(sin5x/(5x)
=5lim(x-->0)(sin5x)/(5x)
=5*1
=5

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