lim x mendekati 4 3-√x²-7/x²-2x-8

jawab


lim (x -4)  {(3 - √(x²-7)(3 + √(x² -7) )} /{(x -4)(x +2)(3 + √(x² - 7)}

lim (x->4) { (9 -x² + 7) / (x- 4) (x+2) (3 + √(x² -7))

lim (x->4)  (16 - x²) /(x - 4)(x+2)(3 +√(x²-7))

lim (x -> 4) (4 - x)(4 +x) / (x -4)(x +2)(3 + √(x² -7))

lim (x->4)   - (x -4) (x + 4)/(x-4)(x +2)(3 + √(x² -7))

lim (x -> 4) - (x +4)/ (x+2) (3 + √(x²-7))

x = 4

lim = -(4 + 4)/ (4+2)(3 +√(16-7))

= - 8/ (6)(3+3)
= - 8 /(36)
= - 2/9