Question

高数函数求极限1.lim(x→0)(x^3-2x^2+3X)/(2x^4+x^3+x)2.lim(x→0)(1-3x)^

Answer 1

1.原式=lim(x→0)(x²-2x+3)/(2x³+x²+1)=3/1=3

2.原式=lim(x→0)[(1-3x)^(1/(-3x))]^[3(x-1)]

=e^{lim(x→0)[3(x-1)}

=e^(-3)=1/e³

3.原式=lim(x→0){[√(1+sinx)-√(1-sinx)]/x}

=lim(x→0){2(sinx/x)/[√(1+sinx)+√(1-sinx)]}

=2[lim(x→0)(sinx/x)]/{lim(x→0)[√(1+sinx)+√(1-sinx)]}

=2*1/2

=1

4.原式=ln{lim(x→0)[(1-2x)^(1/x)]}

=ln{lim(x→0)[(1-2x)^(1/(-2x))]}^(-2)

=ln[e^(-2)]

=-2