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1.=limxsinx/√(2sin²(x²/2))(√(1+xsinx)+1)
=limx²/√2sin(x²/2)*2
=1/√2
2.=limtanx(1-cosx)/x³
=limx(x²/2)/x³
=1/2
3.=limx*2x/(x²+1)=lim2/(1+1/x²)=2
4.=lime(1-e^(cosx-1))(³√(1+x²)²+³√(1+x²)+1)/x²
=lim-3e(cosx-1)/x²
=lim3e(x²/2)/x²
=3e/2
5.=lim(sinx/x-1)/x²
=lim(sinx-x)/x³
=lim(cosx-1)/3x²
=lim-(x²/2)/3x²
=-1/6
6.=e^limxln(1-1/x²)
=e^limx(-1/x²)
=e^0
7.=lim(x+x²-1+e^(-x))/x(1-e^(-x))
=lim(x+x²-1+e^(-x))/x²
=lim(1+2x-e^(-x))/2x
=lim(2+e^(-x))/2
=3/2
=limx²/√2sin(x²/2)*2
=1/√2
2.=limtanx(1-cosx)/x³
=limx(x²/2)/x³
=1/2
3.=limx*2x/(x²+1)=lim2/(1+1/x²)=2
4.=lime(1-e^(cosx-1))(³√(1+x²)²+³√(1+x²)+1)/x²
=lim-3e(cosx-1)/x²
=lim3e(x²/2)/x²
=3e/2
5.=lim(sinx/x-1)/x²
=lim(sinx-x)/x³
=lim(cosx-1)/3x²
=lim-(x²/2)/3x²
=-1/6
6.=e^limxln(1-1/x²)
=e^limx(-1/x²)
=e^0
7.=lim(x+x²-1+e^(-x))/x(1-e^(-x))
=lim(x+x²-1+e^(-x))/x²
=lim(1+2x-e^(-x))/2x
=lim(2+e^(-x))/2
=3/2
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