+253 Find f(a), f(a+h), and the difference quotient f(a+h)-f(a) where h =0
h
f(x)=x^2+8
+33661 f(a) = a2 + 8
f(a+h) = (a+h)2 + 8 = a2 + 2ah + h2 + 8
So: f(a+h) - f(a) = a2 + 2ah + h2 + 8 - ( a2 + 8) = 2ah + h2
and: (f(a+h) - f(a))/h = 2a + h
(Now if you do take the limit of this as h tends to zero, you are left with just 2a)
+118723 Hi Sally,
This is an introductory lesson in Calculus.
By taking the limit as h tends to 0 Alan has found the differential of f(a). That is f '(a)
f(a)=a2+8
f'(a)=2a
The differential is an equation that gives the value of the gradient of the tangent to the curve for any fixed a value.
It is really neat!
