evaluating limit (x->0.5-) (2x - 1) / |2(X^3) - x^2|

[serenaleesl]

evaluating limit (x->0.5-) (2x-1)/|2(X^3)-x^2|

the answer is -4. but how do i explain the working? do i write

Lim(x->0.5-) (2x-1)/(-2(x^3) + x^2) = Lim(x->0.5-) (2x-1)/(x^2(-2x+1)) = Lim(x->0.5-) (-1/(x^2)) = - 4?

correct?

 

[stapel]

evaluating limit (x->0.5-) (2x-1)/|2(X^3)-x^2|

I will guess that, contrary to accepted mathematical practice, you actually mean "X" and "x" to be the same variable.

Lim(x->0.5-) (2x-1)/(-2(x^3) + x^2)

You might want to justify this somehow, perhaps by discussing the sign of f(x) = 2x[sup:3v27pgko]3[/sup:3v27pgko] - x[sup:3v27pgko]2[/sup:3v27pgko] on the interval between x = 0 and x = 1/2.

= Lim(x->0.5-) (2x-1)/(x^2(-2x+1))

It might be more useful to factor out a -x[sup:3v27pgko]2[/sup:3v27pgko], so that the common factor more-sensibly "cancels".

= Lim(x->0.5-) (-1/(x^2)) = - 4?

If you make the adjustment mentioned above, then this step will make sense (and will allow for the necessary evaluation at x = 1/2).

Eliz.