Question

find ((x^3-4x^2+4x)/(x^2-4))​

Answer 1

Answer:

$\frac{ {x}^{3} - {4x}^{2} + 4x }{ {x}^{2} - 4} \\ = \frac{ {x}^{3} - 2 {x}^{2} - 2 {x}^{2} + 4x}{ {x}^{2} - 4 } \\ = \frac{ {x}^{2}(x - 2) - 2x(x - 2)}{ {(x)}^{2} - {(2)}^{2} } \\ = \frac{( {x}^{2} - 2x)(x - 2)}{(x - 2)(x - 2)} \\ = \frac{ {x}^{2} - 2x}{x - 2}$

Answer 2

Step-by-step explanation:

What is the solution for: Lim x^3-4x^2+4x/ x^2-4 then x=2?

We can solve it by two ways: by algebraically and by using L Hospital's rule.

(1) Using algebra method —

limx→2x3−4x2+4xx2−4

=limx→2x(x2−4x+4)(x+2)(x−2)

=limx→2x(x−2)(x−2)(x+2)(x−2)

=limx→2x(x−2)x+2

=limx→22(2−2)2+2

=0

(2) By L Hospital's rule:

limx→2x3−4x2+4xx2−4

=limx→23x2−8x+42x

=3×2×2−8×2+42×2

=12−16+44

=0