Limits & Continuity · Definitions
Right-Hand Limit
The limit of f(x) as x approaches a from the right (from values greater than a). A two-sided limit exists if and only if both one-sided limits exist and are equal.
- 2 worked examples
- 18 in Limits & Continuity
Worked examples
- For x > 0, |x| = x
- So |x|/x = x/x = 1
Answer: lim(x→0⁺) |x|/x = 1
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Related formulas
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Common questions
What is the Right-Hand Limit?
The limit of f(x) as x approaches a from the right (from values greater than a). A two-sided limit exists if and only if both one-sided limits exist and are equal. It is one of the limits & continuity formulas in the CalcRef reference.
When does the Right-Hand Limit apply?
The Right-Hand Limit holds under this condition: f(x) must be defined on an open interval (a, d) for some d > a.
How do you use the Right-Hand Limit?
Worked example. Find lim(x→0⁺) |x|/x. For x > 0, |x| = x. So |x|/x = x/x = 1. Answer: lim(x→0⁺) |x|/x = 1.
Practice
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