求极限lim x→π(sin3x)/(x-π)和求 - 知识问答

求极限lim x→π(sin3x)/(x-π)和求极限lim x→π/2(1+cosx)secx

1个回答

lim(x→π)[(sin3x)/(x-π)],用洛必达法则
=lim(x→π)[3cos3x]
=3cos(3π)
=3*(-1)
=-3
lim(x→π/2)[(1+cosx)^(secx)]
=lim(x→π/2)[(1+cosx)^(1/cosx)],用y=1/cosx
=lim(y→∞)[(1+1/y)^y]
=e

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