Homework Sourselimh rightarrow 0 f3 h f3h fx x2 1Solutionfxx21 f3321 f
lim_h rightarrow 0 f(3 + h) - f(3)/h = f(x) = x^2 - 1![lim_h rightarrow 0 f(3 + h) - f(3)/h = f(x) = x^2 - 1Solutionf(x)=x2-1 f(3)=32-1 f(3)=8 f(3+h)=(3+h)2-1 f(3+h)=9+6h+h2-1 f(3+h)=8+6h+h2 limh->0[f(3+h)-f(3)]](/WebImages/3/limh-rightarrow-0-f3-h-f3h-fx-x2-1solutionfxx21-f3321-f-968330-1761499205-0.webp "lim_h rightarrow 0 f(3 + h) - f(3)/h = f(x) = x^2 - 1Solutionf(x)=x2-1 f(3)=32-1 f(3)=8 f(3+h)=(3+h)2-1 f(3+h)=9+6h+h2-1 f(3+h)=8+6h+h2 limh->0[f(3+h)-f(3)]")
Solution
f(x)=x2-1
f(3)=32-1
f(3)=8
f(3+h)=(3+h)2-1
f(3+h)=9+6h+h2-1
f(3+h)=8+6h+h2
limh->0[f(3+h)-f(3)]/h
=limh->0[(8+6h+h2)-(8)]/h
=limh->0(6h+h2)/h
=limh->0(6+h)
=6+0
=6
limh->0[f(3+h)-f(3)]/h=6
