How do you evaluate the limit #(1/(3+x)-1/(3-x))/x# as x approaches 0?
1 Answer
Jun 23, 2017
The limit equals
Explanation:
We have:
#L = lim_(x-> 0) ((3 - x)/((3 + x)(3 - x)) - (3 + x)/((3 - x)(x + 3)))/x#
#L = lim_(x->0) (3 - x - 3 - x)/((3+ x)(3 - x)x)#
#L = lim_(x->0) (-2x)/((3 + x)(3 - x)x)#
#L = lim_(x->0) -2/((3+ x)(3 - x)#
#L = -2/(3(3))#
#L = -2/9#
Hopefully this helps!
