Back to: Further Mathematics SS2
The followings are the properties of limits:
(i) lim k = k i e
x2 a
The limit of a constant is the constant itself
(ii) lim [f(x) + f 2 (x) + f3 (x) + … fn(x)]
= lim f1(x) + lim f2 (x) + lim f3 (x) +limfn(x)
x a x a x ax a
i.e
The limit of the sum of a finite number of functions is equal to the sum of their respective limits
lim [f1(x) – f2(x)] = limf1(x) – limf2(x)
x a x a x a x a
EVALUATION
Evaluate lim -> 4 x3 +4x 6
Evaluastelim x -> -2 x+6/ 2x +4
Differentiation From first Principle
The technique adopted in unit 11.3 in finding the derivative of a function from the consideration of the limiting value is called differentiation from first principle.
Example
Find the derivative of f(x) = x2 from first principle.
Solution
f (x) = x2
f(x + x) = ( x + x)2
= x2 + 2x x + ( x)2
f(x + x) – f (x) = (x + x)2 – x2
= x2+ 2x x + ( x)2 – x2
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