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I. The Limit Laws

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 Limits at Infinity & Horizontal Asymptotes Notes 2.6 Definitions of Limits at Large Numbers Theorem • If r > 0 is a rational number then 0 1 lim = x →∞ xr • If r > 0 is a rational number such that xr is defined for all x then 0 1

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