Lim

h->0

f (x+h) - f (x) / h

Evaluate this limit for the given value of x and function f.

f (x) = x², x = - 9

Step-by-step explanation:

f (-9+h) = (-9+h) ² = h²-18h+81

f (-9+h) - f (-9) = h²-18h+81 - 81 because : f (-9) = (-9) ² = 81

f (-9+h) - f (-9) = h²-18h

(f (-9+h) - f (-9)) / h = (h²-18h) / h = h (h-18) / h = h-18

lim (f (-9+h) - f (-9)) / h = lim (h-18 = - 18

h→0 h→0