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Master fundamental calculus concepts through this comprehensive video series covering limits, derivatives, and integrals over 6 hours and 9 minutes of instruction. Learn to find limits from graphs and evaluate them using rationalization techniques, explore the Squeeze Theorem with proofs including the classic limit of sin(x)/x as x approaches zero, and understand the Intermediate Value Theorem for finding zeros. Study limits at infinity and horizontal asymptotes before diving into differentiation rules including the Power Rule, Product Rule, Quotient Rule, and Chain Rule through detailed explanations and master problems. Explore derivatives of trigonometric functions, exponential functions like a^x, logarithmic functions with any base, and inverse functions, while learning techniques like implicit differentiation for finding tangent lines and horizontal tangents. Apply the Extreme Value Theorem and learn to find critical points of trigonometric functions, determine absolute extrema on closed intervals, and understand Rolle's Theorem with its proof. Master the analysis of increasing and decreasing functions, apply the Second Derivative Test for optimization, and solve complex optimization problems using systematic approaches. Study linearizations and linear approximations using tangent lines, then transition to integration with Power Rule integrals and separable first-order differential equations. Practice advanced integration techniques including absolute value integrals and the integral of secant x, with companion exercises available in a separate playlist for additional practice using Stewart's or Larson's Calculus textbooks.
