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|a Functions and graphs, limits, tre coordinate plane, distance, grsphs, lines in a plane, functions, the algebra of functions, limits, continuity; the derivative, velocicity rete of change, tengent lines, techniques for differentiation, an introdction, higher order derivatives, the chain rule and extended power rule, related rates, the product and quotient rule, implicit differentiation, more on related rates; extremum problems and curve sketching, strictly increasing and, strictly decreasing functions, local and adsolute extrema, the antiderivative and the integral, the fundamental theorem of calculus, symmetry, consumer surplus; exponential and logarithmic functions, inverse functions and the natural logarithm, exponential growth and decay; sequences and series, hospital´s rule, sequences, geometic series, hospita´s rule; more on integration, a first order difference equation euler´s method, survival functions and renewal theory; maclaurin- taylor polynomials and series, a more general form of taylor´s theorem, maclaurin series; multivariable calculus, extrema of functios of two variables the method of least squares, lagrange multipliers, double integrals over some non- rectangular regions, interchanging limits; the trigonometric functions, angles, the trigonometric functions, graphs of the trigonometric functions, limits and continuity, derivatives of trigonometric functions, integration.
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