nilai [tex] \lim_{x \to 1} \frac{ \sqrt{ x^{2}+3 }-x-1 }{1 - x^{2} } = ....[/tex] a) -1/2 b) -1/4 c) 0 d) 1/4 e) 1/2

Kelas 11 Matematika
Bab LImit

Lim (√(x² + 3) - x - 1)/(1 - x²))
x→1

= Lim (√(x² + 3) - √(x + 1)²)/((1 + x) (1 - x))
   x→1

= Lim (√(x² + 3) - √(x² + 2x + 1))/(x + 1) . (-x + 1)) . (√(x² + 3) + √(x² + 2x + 1)(√(x² + 3) + √(x² + 2x + 1))
   x→1

= Lim ((x² + 3) - (x² + 2x + 1)) / ((-x - 1) . (x - 1) . (√(x² + 3) + √(x² + 2x + 1))
   x→1

= Lim (-2x + 2) / ((-x - 1) . (x - 1) . (√(x² + 3) + √(x² + 2x + 1))
   x→1

= Lim (-2 (x - 1)) / ((-x - 1) . (x - 1) . (√(x² + 3) + √(x² + 2x + 1))
   x→1

= -2 / ((-1 - 1) . (√(1² + 3) + √(1² + 2 . 1 + 1))
= -2 / (-2 . (√4 + √4))
= 1/(2 + 2)
= 1/4