f(x)=1-3x+x^2 maka lim->0 f(x+h)-f(x)/h

jawab

lim(x-0) f(x+h) - f(x) / h = f'(x)

f(x)  =   1 - 2x + x^2
f'(x) =2x  - 2

f(x) = 1 - 3x + x²

f(x + h) = 1 - 3(x + h) + (x + h)²
f(x + h) = 1 - 3x - 3h + x² + 2hx + h²

lim [h-->0] (f(x + h) - f(x))/h
= lim [h-->0] (1 - 3x - 3h + x² + 2hx + h² - (1 - 3x + x²))/h
= lim [h-->0] (-3h - 2hx + h²)/h
= lim [h-->0] (-3 - 2x + h)
= -3 - 2x
= f'(x)
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