How to evaluate limits #[e^x-(1-x)]/x# as x approaches 0?
#[e^x-(1-x)]/x#
2 Answers
Apr 4, 2018
Explanation:
As
hence, to find its limits, we can use L'Hospital's rule
according to which
=
=
Apr 4, 2018
Recall that
#L = lim_(x-> 0) (1 + x + x^2/2 + x^3/6 + ... -1 + x)/x#
#L = lim_(x-> 0) (2x + x^2/2 + x^3/6 + ...)/x#
#L = lim_(x-> 0) 2 + x/2 + x^2/6 + ...#
#L = 2#
The graph confirms:
Hopefully this helps!