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Sample Lecture Notes - University of Massachusetts Amherst

Math131 calculus I The Limit Laws Notes I. The Limit Laws Assumptions: c is a constant and )(limxfax and )(limxgax exist Direct Substitution Property: If f is a polynomial or rational function and a is in the domain of f, then = )(limxfax Simpler Function Property : If )()(xgxf= when ax then)(lim)(limxgxfaxax =, as long as the limit exists. Limit Law in symbols Limit Law in words 1 )(lim)(lim)]()([limxgxfxgxfaxaxax +=+ The limit of a sum is equal to the sum of the limits. 2 )(lim)(lim)]()([limxgxfxgxfaxaxax = The limit of a difference is equal to the difference of the limits.

Math131 Calculus I The Limit Laws Notes 2.3 I. The Limit Laws Assumptions: c is a constant and f x lim ( ) →x a and g x lim ( ) →x a exist Direct Substitution Property: If f is a polynomial or rational function and a is in the domain of f, then = f x lim ( ) x a

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