一題複選題...

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