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LaaP Defs

Chelsea Hilditch RCA Degree Inglés 3 fichas

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1Right-hand limitSuppose that f is defined on (a, a+R) for some positive real number R. Then we say f(x) tends to l as x tends to a from above if, given any positive real number Ɛ, there exists a positive real number δ such that |f(x)-l|< Ɛ whenever a
2Left-hand limitSuppose that f is defined on (a-R, a) for some positive real number R. Then we say f(x) tends to l as x tends to a from below if, given any positive real number Ɛ, there exists a positive real number δ such that |f(x)-l|< Ɛ whenever a-δ
3Ɛ-δ definition of a limit at a pointSuppose f(x) is defined on (a-R,a)U(a,a+R), for some positive real number R. We say f(x) tends to l as x tends to a if, given any positive real number Ɛ, there exists a positive real number δ such that |f(x)-l|<Ɛ whenever 0<|x-a|<δ