can somebody please explain this problem to me:
lim [ (x(e^(-2x+1))) / ((x^2)+x)]
x-->0
i get 0/0 = undefined
but my teacher tells me that it is not correct.
please help
thank you
No, 0/0 is NOT correct for the limit! It's not even a number. And I surely would not recommend "L'Hopital's rule" for something as simple as this.
$\displaystyle \frac{xe^{-2x+1}}{x^2+ x}= \frac{xe^{-2x+1}}{x(x+1)}$
which is equal to $\displaystyle \frac{e^{-2x+1}}{x+1}$ as long as x is not 0. They have the same limit so just put x= 0 in $\displaystyle \frac{e^{-2x+1}}{x+1}$