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The Limit of a Function (What is the Difference between One-Sided Limits and Two-Sided Limits)
This lecture note clearly explains the conceptual distinction between evaluating one-sided and two-sided limits of a function. It starts by formally defining left-hand and right-hand limits - where the function input approaches the limit point from lower or higher values respectively. Two-sided limits are then introduced as cases where the left and right limits exist and evaluate to the same number. These definitions are reinforced visually by annotated graphs showing inputs getting arbitrarily close to limit points from different directions. The lecture note then provides multiple illustrated examples of using graphs to estimate one-sided and two-sided limits, along with determining function values at points. Step-by-step solutions demonstrate how to carefully inspect graphs to evaluate limits, identify cases where some limits do not exist, and contrast these with computing functional outputs at specific input values. The emphasis is on developing intuition for how the direction of approach makes one-sided limits distinct from two-sided evaluation. The accessible explanations combined with annotated visual examples make this an excellent resource for gaining clarity on this fundamental distinction underlying limits in calculus.
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Specifications
- School: Secondary school
- Course: Geography
- Subject: Calculus
- All documents for this course ›
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- Section: Lecture notes
- Updated on: 01-26-2024
- Made on: 01-10-2024
- Type: .pdf
- Pages: 13
- Language: English
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