Numerical Approach to Limits

AP Calculus · Axiom Academy

LESSON Numerical Approach to Limits Use tables of values to find what a function approaches We can estimate limits by creating a table of function values as x approaches a specific value. The closer we get to that value, the closer f(x) gets to the limit. Let's find by evaluating at values near : Left-Sided and Right-Sided Approaches We can approach from the left (x a): Approaching from the left: x = 1.9, 1.99, 1.999, ... Approaching from the right: x = 2.1, 2.01, 2.001, ... If both approaches give the same result, the two-sided limit exists. Tables are powerful but have limitations: Rounding errors: Calculators round; they don't show exact values Missing behavior: A table might miss oscillations between values Finite precision: You can't actually compute at infinity For example, oscillates wildly as x approaches 0, but a table might miss this if we don't sample densely enough. Practice: Building Your Own Table When finding a limit numerically: Choose x-values getting closer to the target value Look for a pattern in the y-values Check both sides approach the same limit Always verify with a graph or another method

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