kak tolong bantu dong 1-5

Limit

1. lim(x->2) (6x² -7x -5)/(2x² + 3x + 1)
sub x = 2
(24 - 14 - 5)/(8 + 6 + 1)= 5/15 = 1/3

2. lim(x->2) { 2/(x-2) - 8/(x²-4)}
lim (x->2)  {2(x+2) - 8} / (x+2)(x-2)
lim (x->2)  (2x -4)/(x+2)(x-2)
lim (x->2)  2(x-2) /(x+2)(x-2)
lim (x->2) 2/(x+2)
x=2 limit = 2/4 = 1/2

3. lim(x->2) ( 4- x²)/ {3 - √(x²+5)}
lim(x->2) (4-x²)(3 + √(x²+5)) /(9 - x² - 5)
lim(x->2) (4-x²)(3 + √(x²+5)/(4-x²)
lim(x->2) 3 + √(x²+5) =
x= 2 , limit = 3 + √9 = 6

4.lim(x-> 0)  3x / [√(9+x) - √(9-x)] =
lim(x->0) 3x {√(9+x) + √(9-x)} /(9+x - 9 + x)
lim(x->0) 3x {√(9+x) + √(9-x)} / (2x)
lim(x->0)  3/2 {√(9+x) + √(9-x)}
x = 0 , limit = 3/2 (3+3) = 9

5. lim(x-> 4) (x-4)/(√x - 2)
lim(x->4)  (√x -2)(√x + 2) / (√x -2)
lim(x->4) √x + 2
x= 4 ,imit = 2 + 2 = 4