MA100 Chapter 5: Limits, Continuity, Limits at Infinity and Derivatives
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Limits: lim x a closer to a? f (x) =? asks what unique, nite value does the function f (x) approach as the value of x gets closer and. If f (x) does not approach a unique, nite value, then we say the limit does not exist. , , 0 , etc. = + check sign of each factor: unique nite number (i. e. f (a) ) ii) 16 4 x x x + 4 (16 x)(4 + x) 8: also note that left/right handed limits may be determined and: f (x) = l lim x a+ lim x a f (x) = lim x a f (x) = l. A function f (x) is continuous at x = a if lim x a f (x) exists and is equal to f (a). X2 2x 8 (cid:0)81x2(cid:1)1/x x 4. Determine the continuity of f (x) at x = 4. lim x 4 f (x) = lim x 4 .