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AP Calculus AB ยท Unit 1
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Notes snippet
# Introduction to Limits ## Big Idea A limit describes the value a function approaches as the input gets close to a specific number. The function does not have to equal that value at the point itself. ## Worked Example Evaluate lim(x -> 3) (x^2 - 9) / (x - 3) Factor the numerator: x^2 - 9 = (x - 3)(x + 3) Now cancel the common factor: (x - 3)(x + 3) / (x - 3) = x + 3 So the limit is 6. ## Why Students Miss It - plugging in too early and stopping at 0/0 - forgetting to factor before simplifying - confusing the limit with the actual function value
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