Penyelesaian:
lim (√x² – 6x – x + 2)
x￫∞
= lim (√x² – 6x – (x – 2))
x￫∞
= lim (√x² – 6x – lim (x – 2)
x￫∞ x￫∞
= ∞ – ∞
Bentuk sekawan dari (√x² – 6x – (x – 2)) ialah (√x² – 6x + (x – 2)).
Menentukan nilai limit fungsi dengan mengalikan dengan bentuk sekawan:
lim (√x² – 6x – (x – 2))
x￫∞
= lim (√x² – 6x – (x – 2)) × √x² – 6x + (x – 2)
x￫∞ √x² – 6x + (x – 2)
= lim (√x² – 6x)² – (x – 2)²
x￫∞ √x² – 6x + (x – 2)
= lim x² – 6x – (x² – 4x + 4)
x￫∞ √x² – 6x + (x – 2)
= lim x² – 6x – x² + 4x – 4
x￫∞ √x² – 6x + (x – 2)
= lim -2x – 4 ₓ ⅟x
x￫∞ √x² – 6x + (x – 2) ⅟x
= lim -2x × ⅟x – 4 × ⅟x
x￫∞ √x² × ⅟x² – 6x × ⅟x² + (x × ⅟x – 2 × ⅟x)
= lim -2 – 4 × ⅟x
x￫∞ √1 – 6 × ⅟x + (1 – 2 × ⅟x)
-2 – 4 × lim 1
= x￫∞ x
√1 – 6 × lim 1 + (1 – 2 × lim 1)
x￫∞ x x￫∞ x
= -2 – 4 × 0
√1 – 6 × 0 + (1 – 2 × 0)
= -2 – 0
√1 – 0 + (1 – 0)
= -2
√1 + 1
= -2
2
= -1
Kaprikornus, nilai lim (√x² – 6x – x + 2) = -1
x￫∞