Example of right upper semicontinuous function

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SUMMARY

Right upper semicontinuous functions are defined by the property that the upper limit of the function as x approaches a point from the right equals the function's value at that point. Key examples include the absolute value function f(x) = |x|, the exponential function f(x) = e^x, the logarithm function f(x) = log(x), the square root function f(x) = sqrt(x), and trigonometric functions such as f(x) = sin(x) and f(x) = cos(x).

PREREQUISITES
  • Understanding of real-valued functions
  • Knowledge of limits and continuity in calculus
  • Familiarity with basic mathematical functions
  • Concept of upper limits in function analysis
NEXT STEPS
  • Study the properties of semicontinuous functions in detail
  • Explore the implications of right upper semicontinuity in real analysis
  • Investigate applications of right upper semicontinuous functions in optimization problems
  • Learn about related concepts such as lower semicontinuous functions
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Mathematicians, students of calculus, and anyone interested in advanced function analysis will benefit from this discussion on right upper semicontinuous functions.

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I am researching right upper semicontinuous function but I didnt find...Please give some examples...thank a lot
 
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Right upper semicontinuous functions are functions that have the property that, for any x in the domain of the function, the upper limit of the function as x approaches that point from the right is equal to the value of the function at that point. Examples of right upper semicontinuous functions include:1) The absolute value function f(x) = |x|2) The exponential function f(x) = e^x3) The logarithm function f(x) = log(x)4) The square root function f(x) = sqrt(x)5) The trigonometric functions, such as f(x) = sin(x) and f(x) = cos(x)
 

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