Limit - AP Calculus - Lecture Notes, Study notes of Calculus

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Calculus Section 1.2A & 1.3A Notes Key idea: A limit is a value that a function approaches from both sides. Notes LT: Evaluate a limit using a table © 2° TBLSET: Set independent to ASK © 2°" TABLE: Key in x-values and read y-values @ What y-value is the function approaching? « For some homework problems you will need to make your own table. Use the earlier problems to help you select x- values. Examples Find the limit using a table. 1) lim ——— lnvei-1 LO x | -0.01 | -0.001 | -0.0001 | 0 | 0.0001 | 0.001 | 0.01 f(x) |\ 445] (4995) 1.4444] (1 260 | 2.0865. 005 LT: Evaluate a limit using a graph e What value (if any) does the function approach from both sides? e If there isa “jump” or a vertical asymptote, the limit does not exist (DINE). e The limit does not necessarily equal the value of the function! LT: Evaluate a limit analytically e Try to substitute the x-value first. 2) lim x? +2 Gs 4 1/2