The limit of higher number function 1.lim(x→0)(x^3-2x^2+3X)/(2x^4+x^3+x) 2.lim(x→0)(1-3x)^1/x -1 3.lim(x→0)[(√1+sinx)-(√1-sinx)]/x 4.lim(x→0)[ln(1-2x)]/x (depressed, I've been doing a pair of answers for a long time. I'm so sad.)

The limit of higher number function 1.lim(x→0)(x^3-2x^2+3X)/(2x^4+x^3+x) 2.lim(x→0)(1-3x)^1/x -1 3.lim(x→0)[(√1+sinx)-(√1-sinx)]/x 4.lim(x→0)[ln(1-2x)]/x (depressed, I've been doing a pair of answers for a long time. I'm so sad.)

1. The original formula = LIM (x → 0) (X & sup2; - 2x + 3) / (2x & sup3; + X & sup2; + 1) = 3 / 1 = 3
2. The original formula = LIM (x → 0) [(1-3x) ^ (1 / (- 3x))] ^ [3 (x-1)]
=e^{lim(x→0)[3(x-1)}
=e^(-3)=1/e³
3. The original formula = 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. The original formula = ln {LIM (x → 0) [(1-2x) ^ (1 / x)]}
=ln{lim(x→0)[(1-2x)^(1/(-2x))]}^(-2)
=ln[e^(-2)]
=-2