limit on the left

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limit on the left [′lim·ət ȯnthə ′left]

(mathematics)

The limit on the left of the function ƒ at a pointcis the limit of ƒ atcwhich would be obtained if only values ofxless thancwere taken into account; more precisely, it is the numberLwhich has the property that for any positive number ε, there is a positive number δ so that ifxis the domain of ƒ and 0 < (c-x) < δ then |ƒ(x) -L| < ε; denoted byAlso known as left-hand limit.

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