作业帮求极限1.limx→-1(x^3+1)/sin(x+1); 2.limx→0(e^x-e^-x)/(sinx); 3.limx→+∞(ln(1+1/x))/(arccotx);4.limx→∞(tanx-sinx)/(1-cos2x);
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求极限1.limx→-1(x^3+1)/sin(x+1); 2.limx→0(e^x-e^-x)/(sinx); 3.limx→+∞(ln(1+1/x))/(arccotx);4.limx→∞(tanx-sinx)/(1-cos2x);
求极限1.limx→-1(x^3+1)/sin(x+1); 2.limx→0(e^x-e^-x)/(sinx); 3.limx→+∞(ln(1+1/x))/(arccotx);
4.limx→∞(tanx-sinx)/(1-cos2x);
求极限1.limx→-1(x^3+1)/sin(x+1); 2.limx→0(e^x-e^-x)/(sinx); 3.limx→+∞(ln(1+1/x))/(arccotx);4.limx→∞(tanx-sinx)/(1-cos2x);
1、lim[x-->-1] (x³+1)/sin(x+1)
=lim[x-->-1] (x+1)(x²-x+1)/sin(x+1)
=lim[x-->-1] (x²-x+1)
=3
2、limx→0(e^x-e^-x)/(sinx)
=limx→0 e^x(1-e^-2x)/(sinx)
等价无穷小代换
=limx→0 2xe^x/x
=2
3、limx→+∞(ln(1+1/x))/(arccotx)
等价无穷小代换
=limx→+∞ (1/x)/(arccotx)
洛必达法则
=limx→+∞ -(1/x²) / (1/(1+x²))
=limx→+∞ -(1+x²)//x²
=-1
第4题太怪了,应该是x-->0吧?
4.limx→0 (tanx-sinx)/(1-cos2x)
洛必达法则
=limx→0 (sec²x-cosx)/(2sin2x)
等价无穷小代换
=limx→0 (sec²x-cosx)/(4x)
=limx→0 (sec²x-1+1-cosx)/(4x)
=limx→0 (sec²x-1)/(4x)+limx→0 (1-cosx)/(4x)
=limx→0 (tan²x)/(4x)+limx→0 (1-cosx)/(4x)
等价无穷小代换
=limx→0 x²/(4x)+limx→0 1/2*x²/(4x)
=0