Determine the limit as x approaches 0 : sinx/(x^2 - x)?

Question

Thanks

Answer 1

lim(x->0)(sin/(x^2-x))

=lim(x->0)(sin(x)'/(x^2-x)')

=lim(x->0)(cox(x)/(2x-1)

=-1

Answer 2

l'Hopital's rule:

Take the derivative of numerator and denominator separately:

sin x -> cos x

x^2 - x -> 2x - 1

Try again with x = 0: 1 / -1 = -1

Answer 3

sin(x)/(x²-x)

= (sin(x)/x)/(x-1)

As x→0:

sin(x)/x → 1

1/(x-1) → 1/(0-1) = -1

The required limit is 1×(-1) = -1

Answer 4

L Hospital rule:

on differentiating Nr and Dr separately, the problem becomes

lim x-->o  cosx/[2x-1]

hence the answer is -1