If the left or right side limits at x = a are infinite or do not exist, then at x = a there is an essential discontinuity or infinite discontinuity.

At x = 2 there is an essential discontinuity because there is no right side limit.

At x = 2 there is an essential discontinuity because there is no left side limit.

At x = 2 there is an essential discontinuity because the right side limit is infinite.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.