57425_02_ch02_p089-099.qk 11/21/08 10:34 AM Page 89 FPO thomasmayerarchive.com Limits and Derivatives 2 In A Preview of Calculus (page 3) we saw how the idea of a limit underlies ...
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...Ch p qk am page fpo thomasmayerarchive com limits and derivatives in a preview of calculus we saw how the idea limit underlies various branches thus it is appropriate to begin our study by investigating their properties special type that used nd tangents velocities gives rise central differential calcu lus derivative see can be interpreted as rates change situations learn function information about original chapter tangent velocity problems this section arise when attempt curve or an object problem t word derived from latin tangens which means touching line touches other words should have same direction at point contact made precise for circle could simply follow euclid say intersects once only figure more complicated curves deni tion inadequate l b shows two lines passing through on c but certainly does not look like what think hand looks twice specic let s trying parabola y x following example v find equation solution will able soon know its slope m difculty one whereas need points c...