limit 3題

1) lim(x→-∞ )[(2x - 2-x)/(2x + 2-x)]

= lim(x→+∞)[(2-x - 2x)/(2-x + 2x)]

= lim(x→+∞)[(2-2x - 2)/(2-2x + 2)]

= -1

2) lim(x→-∞) [√(4x2+1)]/x

= lim(x→+∞) [√(4x2+1)]/(-x)

= - lim(x→+∞) [√(4x2+1)]/x

= - lim(x→+∞) √[(4x2+1)/x2]

= - lim(x→+∞) √(4 + 1/x2)

= -2

3) lim(x→-∞ ) [ (√(x2+1)]+x

= lim(x→+∞) [ (√(x2+1)] - x

= lim(x→+∞) [ √(x2+1) - x][ √(x2+1) + x]/[ √(x2+1) + x]

= lim(x→+∞) [ (x2+1) - x2]/[ √(x2+1) + x]

= lim(x→+∞) 1/[ √(x2+1) + x]

= 0