تحديد الحدود من الرسوم البيانية

Determining Limits from Graphs

• Finding the limit as x approaches a specific value (e.g., x→1): Graphs are used to determine the limit of a function (f(x)) as x approaches a specific value. The limit often describes the behavior of the function close to a certain x-value.

• One-sided Limits: Limits approaching from one side (e.g., x→1-) indicated by a minus sign are from the left of the value on the x-axis. This represents approaching from smaller x-values. The right-sided limit (e.g., x→1+) is from the right of the value on the x-axis (larger x-values).

• Evaluating Limits from Graphs: Analyze the graph's behavior – look at what the y-values approach as you approach the given x-value. Are the y-values approaching a specific number, or do they fluctuate indefinitely?

• Graph examples: Graphs show functions. The student needs to use these graphs to determine the limit of a function at a certain point or when it approaches from specific sides.

• 2023-2024 Exam: The study materials contain specific examples of determining limits using the graphs from two different exam years.

• Other Sample Questions: The documents feature problems from earlier exams, providing practice with different limit scenarios.

• Necessary skills: The study requires understanding and applying the concept of one-sided limits and how to interpret results from graphs.