tentukan turunan pertama f(x) = 4x²-2 dengan pendekatan limit

f(x) = 4x^2 - 2

Lim (f(x + h) - f(x))/h
h => 0

Lim (4(x + h)^2 - 2 - (4x^2 - 2))/h
h => 0

Lim (4(x^2 + 2xh + h^2) - 2 - 4x^2 + 2) / h
h => 0

Lim (4x^2 + 8xh + 4h^2 - 2 - 4x^2 + 2)/h
h => 0

Lim (8xh + 4h^2)/h
h => 0

Lim (8x + 4h)
h => 0

= 8x + 4(0)

= 8x

Langsung aja y

Cara limit

Lim h→0 f(x+h) - f(x) / h

Lim h→0 4(x+h)² - 2 - (4x²-2) / h

Lim h→0 4(x²+2xh+h²)-2 -4x²+2 / h

Lim h→0 4x² + 8xh + 4h² - 4x² / h

Lim h→0 8xh + 4h² / h

Lim h→0 h(8x + 4h) / h

= 8x + 4(0)
= 8x + 0
= 8x

Semoga berguna +_+