求极限lim(x→0)(cos5x-cos3x)/x2
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求极限lim(x→0)(cos5x-cos3x)/x2
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lim(x→0)(cos5x-cos3x)/x^2
=lim(x→0)(-2sin4x*sinx)/x^2
=-2*lim(x→0)(sin4x*sinx)/x^2
=-2*lim(x→0)[4cosx*sinx+sin4x*cosx]/(2x)
=-lim(x→0)(4sinx+sin4x)/x
=-lim(x→0)(4cosx+4cosx)/1
=-lim(x→0)8cosx
=-8
=lim(x→0)(-2sin4x*sinx)/x^2
=-2*lim(x→0)(sin4x*sinx)/x^2
=-2*lim(x→0)[4cosx*sinx+sin4x*cosx]/(2x)
=-lim(x→0)(4sinx+sin4x)/x
=-lim(x→0)(4cosx+4cosx)/1
=-lim(x→0)8cosx
=-8
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