Vipul: Created page with "==Statement== ===Two-sided limit=== Suppose $f$ is a function and $c$ is a point such that $f$ is defined on both the immediate left and th..."

2011-10-20T20:51:38Z

Created page with "==Statement== ===Two-sided limit=== Suppose <math>f</math> is a function and <math>c</math> is a point such that <math>f</math> is defined on both the immediate left and th..."

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==Statement==

===Two-sided limit===

Suppose <math>f</math> is a [[function]] and <math>c</math> is a point such that <math>f</math> is defined on both the immediate left and the immediate right of <math>c</math>. The '''uniqueness theorem for limits''' states that ''if'' the [[fact about::limit]] of <math>f</math> exists at <math>c</math> (in the sense of existence as a finite real number) then it is unique. In other words:

If <math>\lim_{x \to c} f(x) = L</math> and <math>\lim_{x \to c} f(x) = M</math>, then <math>L = M</math>.

===Left hand limit===

Suppose <math>f</math> is a [[function]] and <math>c</math> is a point such that <math>f</math> is defined on the immediate left of <math>c</math>. The '''uniqueness theorem for left hand limits''' states that ''if'' the left hand limit of <math>f</math> exists at <math>c</math> (in the sense of existence as a finite real number) then it is unique. In other words:

If <math>\lim_{x \to c^-} f(x) = L</math> and <math>\lim_{x \to c^-} f(x) = M</math>, then <math>L = M</math>.

===Right hand limit===

Suppose <math>f</math> is a [[function]] and <math>c</math> is a point such that <math>f</math> is defined on the immediate right of <math>c</math>. The '''uniqueness theorem for right hand limits''' states that ''if'' the right hand limit of <math>f</math> exists at <math>c</math> (in the sense of existence as a finite real number) then it is unique. In other words:

If <math>\lim_{x \to c^+} f(x) = L</math> and <math>\lim_{x \to c^+} f(x) = M</math>, then <math>L = M</math>.

Uniqueness theorem for limits - Revision history

Vipul: Created page with "==Statement== ===Two-sided limit=== Suppose f is a function and c is a point such that f is defined on both the immediate left and th..."

Vipul: Created page with "==Statement== ===Two-sided limit=== Suppose $f$ is a function and $c$ is a point such that $f$ is defined on both the immediate left and th..."