How do you find the limit of #1/(x-1)# as x approaches 1?

1 Answer
Oct 18, 2015

See the explanation.


It is relevant for the limit from which side we approach to specific point; in the other words we have to solve two limits:

Let #epsilon in R^+, epsilon->0#, then:

Form the left:
#lim_(x->1-epsilon) 1/(x-1) = lim_(epsilon->0) 1/(1-epsilon-1) = lim_(epsilon->0) 1/-epsilon = -lim_(epsilon->0) 1/epsilon = -oo#

Form the right:
#lim_(x->1+epsilon) 1/(x-1) = lim_(epsilon->0) 1/(1+epsilon-1) = lim_(epsilon->0) 1/epsilon = +oo#