選項一: lim[k→∞] f(k)/f(k+100) lim[k→∞] k^5+........./(k+100)^5+....... lim[k→∞] k^5+........./k^5+..........= 1/1 = 1
選項二: lim[x→1] f(x)-0 / x-1 = x^4+3x^3+2x^2-3x-3 = 0 選項三: f'(x)=5x^4+8x^3-3x^2-10x f(0.5)=-4.4375 f'(1)=0 ∵f'(0.5)<0, f'(1)<0 ∴x=[0.5,1]為遞減 選項四: ∵f(x)=(x-1)^2(x^3+4x^2+6x+3) ∴當x≧0則f(x)≧0 選項五: f(x)=3 x^2(x^3+2x^2-x-5)=0 x^2(x+1)(x^2+3x+3)=0 有交點為x=0,x=-1 有交點的x滿足x^2+3x+3=0 x=-3±(-3)^0.5 /6(兩虛交點) 故f(x)∩y=0為x=0,-1
_________________ If I have seen farther, it is by standing on the shoulders of the giants.---Newton
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