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Master fundamental calculus concepts through this comprehensive 17-hour 52-minute course covering precalculus foundations through advanced derivative applications. Begin with essential precalculus topics including functions, graphing techniques, function modifications, inverse functions, logarithms, quadratic and rational functions, and trigonometry fundamentals. Progress through limits and continuity by learning to solve various limit types including limits at infinity, infinite limits, trigonometric limits, and one-sided limits, while exploring the precise definition of limits, squeeze theorem, continuity concepts, discontinuity identification, and the intermediate value theorem. Develop proficiency in derivatives starting with the fundamental definition and advancing through derivative rules, chain rule applications, trigonometric derivatives, implicit differentiation, exponential and logarithmic derivatives, plus practical applications for finding tangent and normal lines and modeling exponential growth and decay. Apply derivative knowledge to real-world scenarios through linear approximation techniques, optimization problems including applied optimization challenges, related rates calculations, mean value theorem applications, Newton's method for root finding, L'Hospital's rule for indeterminate forms, and physics and economics applications including motion problems, marginal analysis, and profit maximization strategies.
