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CalculusandAnalyticGeometryI SPRINGSEMESTER2016 INSTRUCTOR:DR.M.O’LEARY 25 January 2016 1.1: A Preview of Calculus We will be solving two problems: ● the tangent line problem (How do you find the slope of a curve) ● and the area problem (How do you find the area under a curve) 1.2: Finding Limits Graphically and Numerically Let f(x) = 2x + 1. What value if any does f(x) approach (get closer and closer to) as x approaches 4 If we look at the graph, we can take a quick guess: (picture here) f(4) = 2(4) + 1 = 9 We can also start by filling out a table: 3.9 8.8 3.99 8.98 3.99 8.998 9 4.001 9.00 2 4.01 9.02 4.1 9.2 The process of finding a number that you are approaching is called finding a limit. When finding limits