Question

Using L'Hospital's rule, solve lim x->0 of e^(x)-1-x/x^(2)

Answer 1

Is all of the text before the "/" the numerator?

Answer 2

Assuming it is, e^(0)-1 = 1 - 1 =0, it is lim x->0 of -x/x^2,
this ends up being 0/0, so we use L'Hospital's again (take derivative of top and bottom individually and take limit again)-->
lim x->0 of -1/(2*x) = -1/0 = -infinity

Answer 3

if this I see it right(use L'H rule twice):
\[\lim (e ^{x}-1-x)/x ^{2}=\lim (e ^{x}-1)/2x=\lim e ^{x}/2=1/2\]

Answer 4

Oops, inik is correct

Answer 5

sorry...i typed it in wrong myininaya. the stuff before the "/" is the numerator, and the x^2 is the denominator.

Answer 6

ok

Answer 7

what inik has is corrrect then