MAT135H1 Study Guide - Final Guide: Squeeze Theorem, Intermediate Value Theorem, Mean Value Theorem
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MAT135H1 Full Course Notes
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Rolle"s theorem h lim h 0 f(x+h) f(x) Limit - the y-value a function approaches when it approaches an x-value. One-sided limits: only looking at one side in question. The limit lim x a f(x) = l will exist iff both the right and left handed limits are equal. Limit properties f(x) = l f(x) = l: constant rule, sum or difference, product rule, quotient rule, power rule, special power rule, limit of a constant is the constant. 9. lim x a = a lim x a x n = a n. Ex: compute lim as x -2 (3x 2 +5x -9) lim[cf(x)] = c limf(x) lim[f(x) +- g(x)] = lim f(x) +- lim g(x) lim[f(x)g(x)] = limf(x)limg(x) lim [ if limg(x) lim[f(x)] n = [limf(x)] n lim n. =/ 0 f(x) g(x) lim 3x 2 + lim5x - lim9. 1: 3limx 2 + 5limx - lim9, 3(-2) 2 +5(-2) -9 = -7.
