Tolong dong yg senior bantu jawab dong besok uda di kumpul entar aku follow deh
limit tak hingga
L = lim x→∞ √(ax² + bx + c) – √(px² + qx + r)
a = p → L = (b – q)/2√a
nilai c diabaikan
a.
lim x→∞ √(x² + 6x) – (x – 4)
= lim x→∞ √(x² + 6x) – √(x – 4)²
= lim x→∞ √(x² + 6x) – √(x² – 8x + 16)
= (6 – (-8))/2√1
= 14/2
= 7
b.
lim x→∞ (3x – 1) – √(9x² – 8x + 1)
= lim x→∞ √(3x – 1)² – √(9x² – 8x + 1)
= lim x→∞ √(9x² – 6x + 1) – √(9x² – 8x + 1)
= (-6 – (-8))/2√9
= 2/(2.3)
= 1/3
c.
a < p → L = – ∞
lim x→∞ √(4x² + 3x – 2) – (3x + 2)
= lim x→∞ √(4x² + 3x – 2) – √(3x + 2)²
= lim x→∞ √(4x² + 3x – 2) – √(9x² + 12x + 4)
= – ∞
d.
a > p → L = + ∞
lim x→∞ (2x – 3) – √(x² – 3x + 2)
= lim x→∞ √(2x – 3)² – √(x² – 3x + 2)
= lim x→∞ √(4x² – 12x + 9) – √(x² – 3x + 2)
= + ∞
e.
lim x→∞ (x – 2) – √(x² – 4x + 3)
= lim x→∞ √(x – 2) – √(x² – 4x + 3)
= lim x→∞ √(x² – 4x + 4) – √(x² – 4x + 3)
= (-4 – (-4))/2√1
= 0/2
= 0