Math 9C Sec 2.2

Math 9C Sec 2.2 - x a f x L Ex Find lim → x 01x2 if the...

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Section 2.2 Definition: lim f(x)=L if we can make tge values of f(x) arbitrarily close to L by taking x to be sufficiently close to a1 but not equal to a. Basically, x gets closer and closer to a1 f(x) gets closer and closer to L Notation: lim f(x)=L x→a Note: When evaluating the limit we don’t use x=a, in fact, f(x) can be undefined at a, but the limit can exist. Ex) Guess the value of the limit lim - - x 1x2 1 x→1 = lim x-1/(x-1)(x+1)=lim 1/x+1=1/2 Definition: lim → - = x a fx L if we can get f(x) arbitrarily close to L by taking values of x sufficiently close to but strictly less than a. Therom: lim = x afx L if and only if lim → - = x a fx lim → + ( )=
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Unformatted text preview: x a f x L Ex) Find lim → x 01x2 if the limit exists lim → -= ∞ x 0 1x2 lim → + = ∞ x 0 1x2 Definition: Let f be a function defined on both sides of a except possibly at a lim → =∞ x afx if the values of f(x) can be made arbitrarily large by taking x sufficiently close to a1 but not equal to a. Any combo of a+ and a- as well as ∞ and -∞. Definition: x=a is a vertical asymptote if one of the following happens. lim → -x a f(x)=∞ lim → -x a f(x)=-∞ lim → + x a f(x)=∞ lim → + x a f(x)=-∞ Ex) Find lim → + - =∞ x 3 2x x 3 and lim → --x 3 2xx 3 =-∞ Homework: 1, 2, 4,5,6, 13, 15, 25-31 odd...
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Math 9C Sec 2.2 - x a f x L Ex Find lim → x 01x2 if the...

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