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Review Notes for Final Exam.pdf

6 Pages

Course Code
MATH 157
Shiva Gol Tabaghi

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Review Notes Lxflim1 Limit of a function we writeax and say the limit of fx as x approaches a equals L if we can make the value of fx arbitrary close to L as close to L as we like by taking x to be sufficiently close to a on either side of a but not equal to aFact LxfandLxfLxflimlimlim axaxaxSpecial Limits sin1xn1lim7182821limee xn0xn 2 Limit definition of Continuity of a function A function is continuous at a number aifafxflim axxflimafxflimNote a belongs to the domain of fb existcaxaxDiscontinuity of a function at a If1 f is defined on an open interval containing a except perhaps at a and2 f is not continuous at a we say that f is discontinuous at aTheorem Intermediate value theorem Suppose that f is continuous on the closed interval ab and let N be any number between fa and fb where fa fb Then there exists a number c in ab such that fcNTheorem Existence of Zeros of a continuous function If f is a continuous function on a closed interval ab and if fa and fb have opposite signs then there is at least on solution of the equation fx0 in the interval ab
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