What is value of lim x tends to 0 [log (5+x) -log(5-x)]/ x. ?

1 Answer
Ananda Dasgupta
Jul 5, 2018

#2/5#

Explanation:

#lim_{x to 0}(log(5+x)-log(5-x))/x#
#qquad = lim_{x to 0}(log(5+x)-log 5 +log 5 -log(5-x))/x#
#qquad = lim_{x to 0}[(log(5+x)-log 5)/x + (log(5+(-x))-log 5)/(-x)]#
#qquad = lim_{x to 0}(log(5+x)-log 5)/x#
#qquadqquad+ lim_{(-x) to 0}(log(5+(-x))-log 5)/(-x) #
#qquad = d/dx log(x) ]_{x=5} + d/dx log(x) ]_{x=5}#
#qquad = 2/5#

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