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

Answer 1

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#

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Answer 2

Scarlett Allison

To find the limit of 1/(x-1) as x approaches 1, we can substitute the value of x into the expression. However, this would result in division by zero, which is undefined. Therefore, the limit does not exist.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.