1.lim x→0 3x/(sinx-x)2.lim x→0 (1-cosmx)/x^23.lim x→0 sin4x/[(√x+2)-√2]4.lim h →0 [sin(x+h)-sin(x-h)]/h
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1.limx→03x/(sinx-x)2.limx→0(1-cosmx)/x^23.limx→0sin4x/[(√x+2)-√2]4.limh→0[sin(x+h)-sin(x-h)]/h1.limx
1.lim x→0 3x/(sinx-x)2.lim x→0 (1-cosmx)/x^23.lim x→0 sin4x/[(√x+2)-√2]4.lim h →0 [sin(x+h)-sin(x-h)]/h
1.lim x→0 3x/(sinx-x)
2.lim x→0 (1-cosmx)/x^2
3.lim x→0 sin4x/[(√x+2)-√2]
4.lim h →0 [sin(x+h)-sin(x-h)]/h
1.lim x→0 3x/(sinx-x)2.lim x→0 (1-cosmx)/x^23.lim x→0 sin4x/[(√x+2)-√2]4.lim h →0 [sin(x+h)-sin(x-h)]/h
lim x→0 3x/(sinx-x)
洛必达
=lim 3/cosx-1
->∞
2.lim x→0 (1-cosmx)/x^2
=lim 2sin^2(mx/2)/x^2
=lim 2(mx/2)^2/x^2
=m^2/2
3 lim x→0 sin4x/[(√x+2)-√2]
=lim sin4x((√x+2)+√2)/x
=8√2
4 lim h →0 [sin(x+h)-sin(x-h)]/h
=lim h →0 [sin(x+h)-sinx+sinx-sin(x-h)]/h
=sin'x+sin'x
=cosx+cosx
=2cosx
lim (x→0)x-sinx/x
lim (x->0) 3x/(sinx-x)
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