Question

Matematika
Lim
x => ∞

Answer 1

Karena limit x mendekati tak hingga, maka :

f (x) / g (x) = f ' (x) / g ' (x) = f '' (x) / g '' (x) = .... dst.

limit x mendekati tak hingga

3x√x - x - 7
5 + 4x + x³

f (x) = 3x√x - x - 7
= 3x(x)¹/² - x - 7
= 3x³/² - x - 7
f ' (x) = 3/2.3√x - 1
f ' (x) 9√x / 2 - 1
f ' (x) = (9√x - 2) / 2

g (x) = 5 + 4x + x³/²
g (x) = x³/² + 4x + 5
g ' (x) = 3/2√x + 4
g ' (x) = (3√x + 8) / 2

f ' (x) / g ' (x)
= ((9√x - 2) / 2) / ((3√x + 8) / 2)
= (9√x - 2) / (3√x + 8)

f ' (x) = 9√x - 2
f ' (x) = 9x¹/² - 2
f '' (x) = (9/2) / √x

g ' (x) = 3√x + 8
g ' (x) = 3x¹/² + 8
g '' (x) = (3/2) / √x

f '' (x) / g '' (x) = ((9/2) / √x) / ((3/2) / √x))
= (9/2) / (3/2)
= 9/3
= 3