tolong bantu cari k limit x→∞ [ √(x²+k(x+2)) - √(x(x+1)) ] = 2 pakai cara

kalo ga salah sih bgtu yaa

limit  √ {x² + k (x + 2) } - √{x (x + 1)} = 2
x⇒∞

limit  √(x² + kx + 2) - √(x² + x) = 2
x⇒∞

limit [√(x² +kx +2) - √(x² +x)] [√(x² +kx +2) + √(x² + x)] /√(x² + kx + 2) +√(x² + x) = 2
x⇒∞

limit  {x² + kx + 2 - (x² + x) } / {√(x² + kx + 2) + √(x² + x)} = 2
x⇒∞

limit (x² + kx + 2 - x² - x) / {√x² + kx + 2) + √(x² + x)} = 2
x⇒∞

limit (kx - x + 2) / {√(x² + kx + 2) + √(x² + x)} = 2
x⇒∞

limit x (k - 1 + 2/x) / { x√(1 + k/x + 2/x²) + x√(1 + 1/x)} = 2   ... bagi degan x
x⇒∞

limit (k - 1 + 2/x) / {√(1 + k/x + 2/x²) + √(1 + 1/x) } = 2
x⇒∞

( k - 1 + 2/∞) / {√(1 + k/∞ + 2/∞²) + √(1 + 1/∞) = 2

(k - 1 + 0) / {√(1 + 0 + 0) + √(1 + 0)} = 2

(k - 1) / (√1  + √1) = 2

(k - 1) / (1 + 1) = 2

(k - 1) / 2 = 2

k - 1 = 4
     k = 4 + 1
     k = 5